����JFIF�����%%��� }!1AQa"q2���#B��R��$3br� %&'()*456789:CDEFGHIJSTUVWXYZcdefghijstuvwxyz������������������������������������������������������������������������� w!1AQaq"2�B���� #3R�br� $4�%�&'()*56789:CDEFGHIJSTUVWXYZcdefghijstuvwxyz��������������������������������������������������������������������������?��(�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� �@���o�E��?�?����ο�U_�P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@ _�z�����������g_ڪ�?��(�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (��?�/�=[�Qe�����g����U@��P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@����(���g���Y������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���V��Y|����Y����UP��@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P����,�����,��u������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���տ�_�����:��T�~�@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@������/���?��j���h�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� �@���o�E��?�?����ο�U_�P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@ _�z�����������g_ڪ�?��(�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (��?�/�=[�Qe�����g����U@��P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@����(���g���Y������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���V��Y|����Y����UP��@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P����,�����,��u������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���տ�_�����:��T�~�@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@������/���?��j���h�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� �@���o�E��?�?����ο�U_�P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@ _�z�����������g_ڪ�?��(�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (��?�/�=[�Qe�����g����U@��P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@����(���g���Y������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���V��Y|����Y����UP��@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P����,�����,��u������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���տ�_�����:��T�~�@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@������/���?��j���h�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� �@���o�E��?�?����ο�U_�P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@ _�z�����������g_ڪ�?��(�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (��?�/�=[�Qe�����g����U@��P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@����(���g���Y������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���V��Y|����Y����UP��@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P����,�����,��u������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���տ�_�����:��T�~�@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@������/���?��j���h�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� �@���o�E��?�?����ο�U_�P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@ _�z�����������g_ڪ�?��(�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (��?�/�=[�Qe�����g����U@��P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@����(���g���Y������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���V��Y|����Y����UP��@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P����,�����,��u������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���տ�_�����:��T�~�@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@������/���?��j���h�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� �@���o�E��?�?����ο�U_�P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@ _�z�����������g_ڪ�?��(�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (��?�/�=[�Qe�����g����U@��P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@����(���g���Y������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���V��Y|����Y����UP��@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P����,�����,��u������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���տ�_�����:��T�~�@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@������/���?��j���h�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� �@���o�E��?�?����ο�U_�P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@ _�z�����������g_ڪ�?��(�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (��?�/�=[�Qe�����g����U@��P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@����(���g���Y������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���V��Y|����Y����UP��@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P����,�����,��u������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���տ�_�����:��T�~�@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@������/���?��j���h�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� �@���o�E��?�?����ο�U_�P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@ _�z�����������g_ڪ�?��(�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (��?�/�=[�Qe�����g����U@��P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@����(���g���Y������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���V��Y|����Y����UP��@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P����,�����,��u������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���տ�_�����:��T�~�@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@������/���?��j���h�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� �@���o�E��?�?����ο�U_�P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@ _�z�����������g_ڪ�?��(�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (��?�/�=[�Qe�����g����U@��P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@����(���g���Y������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���V��Y|��O�������h�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� �@��o�E��/�?��ߵE_�P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@ ?�z�����������goڢ�?��(�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (��?��=[�Qg�����o����Q@��P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@����(���g���Y������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���V��Y�����[����TP��@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P����,���|-��v��(���� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���տ�������;~��P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@�������?�_�����j������ (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� �@��o�E��/�?��ߵE_�P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@ ?�z�����������goڢ�?��(�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (��?��=[�Qg�����o����Q@��P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@����(���g���Y������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���V��Y�����[����TP��@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P����,���|-��v��(���� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���տ�������;~��P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@�������?�_�����j������ (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� �@��o�E��/�?��ߵE_�P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@ ?�z�����������goڢ�?��(�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (��?��=[�Qg�����o����Q@��P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@����(���g���Y������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���V��Y�����[����TP��@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P����,��������ο�O�P��@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P����,�����,��u������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���տ�_�����:��T�~�@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@������/���?��j���h�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� �@���o�E��?�?����ο�U_�P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@ _�z�����������g_ڪ�?��(�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (��?�/�=[�Qe�����g����U@��P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@����(���g���Y������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���V��Y|����Y����UP��@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P����,�����,��u������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���տ�_�����:��T�~�@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@������/���?��j���h�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� �@���o�E��?�?����ο�U_�P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@ _�z�����������g_ڪ�?��(�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (��?�/�=[�Qe�����g����U@��P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@����(���g���Y������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���V��Y|����Y����UP��@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P����,�����,��u������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���տ�_�����:��T�~�@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@������/���?��j���h�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� �@���o�E��?�?����ο�U_�P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@ _�z�����������g_ڪ�?��(�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (��?�/�=[�Qe�����g����U@��P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@����(���g���Y������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���V��Y|����Y����UP��@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P����,�����,��u������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���տ�_�����:��T�~�@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@������/���?��j���h�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� �@���o�E��?�?����ο�U_�P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@ _�z�����������g_ڪ�?��(�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (��?�/�=[�Qe�����g����U@��P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@����(���g���Y������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���V��Y|����Y����UP��@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P����,�����,��u������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���տ�_�����:��T�~�@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@������/���?��j���h�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� �@���o�E��?�?����ο�U_�P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@ _�z�����������g_ڪ�?��(�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (��?�/�=[�Qe�����g����U@��P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@������k�w���~���v��������� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (�� (���տ�_�����:��T�~�@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@P@������/���?��j�?�5o�%��?��� g����U@�����&O3�����a�;�^=�wH���D��/��*� �fX�I���,������k?g_���?�5o�%��?��� g����U@�F�����������*������?�o�}��Τ~g��ʀ�#V��Y������~ο�T�j��K/� ������������z��������#;�~���A�;��� w�F�����������*���տ��_�@�o��5����EU������������u�誠��W��[�����������O��?jW���@��տ���@�o��5����EM������������v�訠�#V��Y�������������V��Zv��~����vw�~���c�Q@���,��~���kgo���?�5o�%��/��� o����Q@��o�%�>�ߤ���߳����S������?��o�%�~�ߠ�d�߳����S����g�P��j��K?� _������������[� g�D����[�;�TP7���������'Ѿ���=��;/�P��j��K?� _������������[� g�D����[�;�TP���,��~���kgo���a������۔���B{���ea�`T�+ �n%Ц �����j��K?� _������������[� g�D����[�;�TP���,��~���kgo����?���%�/�~�����#����x��c�~�q�v�t`ȫ��_'h���������'�]�;{s� Pp=N= 5���%�����ڜs�����=���J��A@�����Kp�b��}��X�����4g v+:�Բ�+60�ʩ,� @�����������I �uO�����ToUv��bgUl�cP�T?�#V��Y������������j��K?� _����������!��X��]���������TK�|4��`� ��#��P\y��aa >NgL��j��K?� _������������[� g�D����[�;�TP���,��~���kgo���o�F�����$��ہ�� ��vݞr6��S�q''*02���[� g�D����[�;�TP���,��~���kgo���?�5o�%��/��� o����Q@�F�����������*(��տ���@�o��5����EE������������v�訠��������~1�o���}G�L�������5o�%��/��� o����Q@�F�����������*(��տ���@�o��5����EE5����%�˷���r�v����y�\~���)(?0���=[� i����>��gc��N=����5o�%��/��� o����Q@�F�����������*(��W��Z�l����m#���X�wn_�j`0C6윅����5o�%��/��� o����Q@��տ��y9���gbO�G�5@�n�>���#V��Y������~ο�T��V��Y����9�gc��s�T.�?Z_��[� e�D����Y�:��UP���,������k?g_����_�=_� n�~~�rI������w�,"~ԓ�!72���)( u��#V��Y������~ο�T�j��K/� ��������������K
�����Kr_���}�De>~��Z=��pjX�n[p(�"� �a,Ub�/�×�<����;��<�����K>��o���[�:����V���,��$��ϧ�*�����5O����տ��_�@�o��5����EU5��o�%����?�ꜜm�_�;>Gbs�S�����@��տ��_�@�o��5����EU ��տ��}�~�����v?�������-��o�l��~�ȥ�v����r��B1���@��տ���A�?����ggP��c�S�`@%�*����տ��_�@�o��5����EU������������u�誠7���� O���!c�|0��ёv��4�+�X�Vx�RX3��8����K>��o���[�:���u#�x��#V��Y������~ο�T�j��K/� ������������[� e�D����Y�:��UP���,������k?g_���O��[� g�D����[�:��T��=_� k����~��k����c�;����.8����c��z��Ͽ�/��zc�o����F?Z_��[� e�D����Y�:��UP���,������k?g_���C���,�v����v�o���H������(�z���w�/�����v ��T.G��Ϡ���տ��_�@�o��5����EU������������u�誠��W��[��'����%��o���:�Cڕ�R̀���j���������?�o���[�;������g0q�?��o�%�>o�_��>�gf����~4�������������u�誠�z���7�/��o���������_��[� e�D����Y�:��UP���,������k?g_���C���,�|�����o��;�Ԟ��9�l�z��ؠ3|��O�X�~���;~�q����Z�F�����������*���տ��_�@�o��5����EU!��տ��}�~����-��G��I�T�������������u�誠�#V��Y������~ο�T�j��K/� ����������#�=_� n|���KbB�gtdM��"�ڒA#n�63�6�m�P�����,���/���gS�u����#�9��5o�%��?��� g����U@��o�%�o�_�����u��'�������?��o��� ���3��?go���|m�ڇ���-S�O��x��>���^�����7����x�]_�>�qke>���m��4��7P�Yހ��
0byt3m1n1
0byt3m1n1
Path:
/
hermes
/
bosweb
/
web
/
b2920
/
robertgrove.netfirms.com
/
rk72z8wr
/
cache
/
[
Home
]
File: 13219b9c6a82bebc7a31df72142cab4a
a:5:{s:8:"template";s:1357:"<!DOCTYPE html> <html lang="en"> <head> <meta charset="utf-8"> <meta content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no" name="viewport"> <title>{{ keyword }}</title> <style rel="stylesheet" type="text/css">body,div,html{margin:0;padding:0;border:0;font-size:100%;vertical-align:baseline}html{font-size:100%;overflow-y:scroll;-webkit-text-size-adjust:100%;-ms-text-size-adjust:100%}*,:after,:before{-webkit-box-sizing:border-box;-moz-box-sizing:border-box;box-sizing:border-box}body{font-family:Karla,Arial,sans-serif;font-size:100%;line-height:1.6;background-repeat:no-repeat;background-attachment:fixed;background-position:center center;-webkit-background-size:cover;-moz-background-size:cover;background-size:cover}</style> </head> <body class="lightbox nav-dropdown-has-arrow"> <div id="wrapper"> <header class="header has-sticky sticky-jump" id="header"> <div class="header-wrapper"> <div class="header-bg-container fill"> <h2>{{ keyword }}</h2> </div> </div> </header> <main class="" id="main"> {{ text }} </main> <footer class="footer-wrapper" id="footer"> {{ links }} <div class="absolute-footer dark medium-text-center text-center"> <div class="container clearfix"> <div class="footer-primary pull-left"> <div class="copyright-footer"> {{ keyword }} 2022</div> </div> </div> </div> </footer> </div> </body> </html>";s:4:"text";s:23270:"To understand parameterisation of curves and to find arc length. Problem 5E. 36 Lectures Average 31 minutes each 1 A Visual Introduction to 3-D Calculus 2 Functions of Several Variables 3 Limits, Continuity, and Partial Derivatives 4 Partial DerivativesOne Variable at a Time 5 Total Differentials and Chain Rules 6 Extrema of Functions of Two Variables 7 Applications to Optimization Problems Learn multivariable calculus for freederivatives and integrals of multivariable functions, application problems, and more. In this course, you will learn how to set up, solve, and interpret many types of multivariable integrals: triple integrals in cartesian, cylindrical, and spherical coordinates. able problems that have one-variable counterparts. Linear Algebra is almost universally considered dreadfully boring, but it's not too difficult. Multivariable Calculus is an extension of the Calculus that you studied during your High School days to functions of several variables. Supplementary Notes Rossi Section 1834. In slightly fancier lan-guage, single variable calculus is the study of functions f : R !R. Search: Multivariable Chain Rule Calculator. This collection was compiled in the process of teaching multivariable calculus at Brunel University London during the years 2014-2016. The real number system. Functions that take two or more input variables are called "multivariate.". Multivariable calculus problems and solutions pdf. Understanding Multivariable Calculus Problems Solutions And Tips Addeddate 2021-06-30 06:24:18 Identifier understanding-multivariable-calculus-problems-solutions-and-tips Identifier-ark ark:/13960/t20d6r325 Ocr tesseract 5..-alpha-20201231-10-g1236 Ocr_autonomous true Ocr_detected_lang en Ocr_detected_lang_conf 1.0000 For example, f ( x, y) = x 2 + y. f (x, y) = x^2 + y f (x,y) = x2 + y is a multivariate function. How to apply Multivariable Calculus to real life problems. a) When you . Multivariate calculus is a challanging course. which is a central focus of what we call the calculus of functions of a single variable, in this case. The key operations . So, if you are planning to make a career in . Single variable calculus is the study of functions of one variable. Complete the book problems from Chapters 10.4 and 9.1. We are often faced with problems whereby we are attempting to predict a variable that is dependent on multiple variables. Calculus problems with detailed, solutions. Section11.1 Vectors In The Plane 11.2 Space Coordinates And Vectors In Space 11.3 The Dot Product Of Two Vectors 11.4 The Cross Product Of Two Vectors In Space 11.5 Lines And Planes In Space 11.6 Surfaces In Space 11.7 Cylindrical And Spherical Coordinates Chapter Questions. Calculus 3 (or multivariable calculus) stresses visualization heavily, as . The second part is an introduction to linear algebra. These notes are based on lectures from Math 32AH, an honors multivariable differential calculus course at UCLA I taught in the fall of 2020. but the problems in the books recommended were not hard enough. Many of the problems and gures are taken directly from the Mathematics 5 book, written by Rick Parris and other members of the PEA Mathematics Department. Emphasizing the Rule of Fourviewing problems graphically, numerically, symbolically, and . Change is an essential part of our world, and calculus helps us quantify it. Multivariable Calculus. Problem 6E. J. Marsden, A. Weinstein, Calculus III. Berkeley's multivariable calculus course. Two and three dimensions will also permit easier Multivariable Calculus has far reaching applications in Physics, Engineering and advanced Computer Science. a) When you have two lines in 3d space (so xyz space), what are the possibilities? The curriculum tackles lessons with growing levels of difficulty and solidifies the theory before moving to problems. The introduction of each worksheet very briey summarizes the main ideas but is not intended as a substitute for the textbook or lectures. Study guide and practice problems on 'Multivariable calculus'. The course opens with a unit on vectors, which introduces students to this critical component of advanced . Two projects are included for students to experience computer algebra. Distance Calculus Courses. strong treatment of multivariable maximum-minimum problems in Sections 13 Triple integrals Calculus 3 Lecture 13 The PowerMod Calculator, or Modular Exponentiation Calculator, calculates online a^b mod n step-by-step , the chain rule in matrix form) , the chain rule in matrix form). $202.25. . The introduction of each worksheet very briey summarizes the main ideas but is not intended as a substitute for the textbook or lectures. Learn how tools like the . Multivariable Calculus courses from top universities and . Roughly speaking the book is organized into three main parts corresponding to the type of function being studied: vector . Most sections should have a range of difficulty levels in . Multivariable calculus is the generalization of integrals and derivatives to functions of multiple variables. However, if you've taken differential and integral calculus you should be fine. Examples of 2D Parametric Curves (13 minutes) (Part of Section . Expect to not understand a lot without putting significant time and effort into . To familiarise with calculus of multiple variables. The school has recommended Multivariable Calculus from Johns Hopkins University (CTY Program) because I completed AP Calculus BC in 10th grade and took AP Statistics in 11th grade and I can't really "rest" and do nothing for 12th . Calculus III (Multivariable Calculus) (Udemy) If you are looking forward to online matters to supplement your college classes or even a standalone reference for STEM majors, this tutorial might come in handy. Specically, the multivari-able chain rule helps with change of variable in partial dierential equations, a multivariable analogue of the max/min test helps with optimization, and the multivariable derivative of a scalar-valued function helps to nd tangent planes and trajectories. There is a newer edition of this item: Multivariable Calculus. We extend the Fundamental Theorem of Calculus to multiple dimensions, and the course will culminate in Green's, Stokes' and Gauss' Theorems. The topics include curves, differentiability and partial derivatives, multiple integrals, vector fields, line and surface integrals, and the theorems of Green, Stokes, and Gauss. I took 4 AP courses in my junior year and got good scores. Math majors should consider MAT203 instead. The patient explanations, superb exercises, focus on problem . That is, in single variable calculus you study functions of a single independent variable y=f(x). Combine that with the demands and expectations of a millennial college student and even Terence Tao would pull his hair out. The problems in the midterm and the final were more difficult than most of the problems in the book and I studied mostly by doing the practice tests. Additional Problems for Multivariable Calculus Mariano Echeverria 1 Vectors and Curves 1. Course Description This course covers differential, integral and vector calculus for functions of more than one variable. Calc 3 wasn't as hard for me as Calc 2. Di erential calculus for functions whose domain is one-dimensional turns out to be very similar to elementary calculus no matter how large the dimension of the range. If you have taken multi in high school, this course will undoubtedly deepen your understanding and address topics you most likely would've skipped or only skimmed over in high school. Problem 4E. Berkeley's multivariable calculus course. I am a rising senior, who took 7 AP courses in total. Specically, the multivari-able chain rule helps with change of variable in partial dierential equations, a multivariable analogue of the max/min test helps with optimization, and the multivariable derivative of a scalar-valued function helps to nd tangent planes and trajectories. Additional Problems for Multivariable Calculus Mariano Echeverria 1 Vectors and Curves 1. baileyj57 April 10, 2015, 4:01pm #16. Computer algebra The materials have been organized to support independent study. As its name suggests, multivariable calculus is the extension of calculus to more than one variable. Instructor-led. A river flows with speed $10$ m/s in the northeast direction. You will receive incredibly detailed scoring results at the end of your Multivariable Calculus practice test to help you identify your . . Basically I'm looking for a difficult, thorough version of a calc 3 text. Calculus III. In the first part of this course Multivariable Calculus is explained by focusing on understanding the key concepts rather than learning the formulas and/or exercises by rote. It's a lot like moving from (a+2) in algebra to (a^2 + 2ab + b^2). Springer, 1985. Besides, interesting proofs will be . d) Or Specically, the multivari-able chain rule helps with change of variable in partial dierential equations, a multivariable analogue of the max/min test helps with optimization, and the multivariable derivative of a scalar-valued function helps to nd tangent planes and trajectories. This lecture note is closely following the part of multivariable calculus in Stewart's book [7]. We can construct the operation of addition in the product set R2 by using the notion of addition in each factor R of R2 and forming an addition in R2 component-wise: (a;b)+(c;d)=(a+c;b+d): To see how calculus applies in situations described by more than one variable, we study vectors, lines, planes, and parameterization of curves and surfaces; partial derivatives, directional derivatives, and gradients; optimization and critical point analy. Complete the book problems from Chapters 10.4 and 9.1. Keep up with the class, do the homework, and get an A. Here are a set of practice problems for the Calculus III notes. At the end of the course the student will be able to. MAT201 is an introduction to multivariable calculus designed for students who have already taken calculus either in high school or at Princeton. A particular boat can propel itself at speed $20$ m/s relative to the water. The course is expected to enable the students. Note how the y Curves in R3 1-2: Practice Problems 4, PDF 3D plot tool 7 Course description Course description. Multivariable Calculus: Early Transcendentals Elementary Linear Programming with Applications Using an extremely clear and informal approach, this book introduces readers to a rigorous understanding of mathematical analysis and presents challenging math concepts as clearly as possible. The third part of the book combines techniques from calculus and linear algebra and contains discussions of some of the most elegant results in calculus including Taylor's theorem in "n" variables, the multivariable mean value theorem . Skim through Sections 10.7 and 10.5 of the book. Calc II is Series, Vectors, and Multivariable Calculus. Our completely free Multivariable Calculus practice tests are the perfect way to brush up your skills. The ideal resource for promoting active learning in flipped classroom environments, Calculus: Multivariable, 8th Edition brings calculus to real life with relevant examples and a variety of problems with applications from the physical sciences, economics, health, biology, engineering, and economics. Two lines on the xy plane either intersect at a point or are parallel. June 21 - August 5, 2022. Multivariable Calculus The problems in this text This set of problems is based on the curriculum at Phillips Exeter Academy, a private high school in Exeter, NH. On the other hand, it requires a stronger geometric intuition because there are more ways to do things in two or three dimensions than there are in one. (10) Only 1 left in stock - order soon. At . Understanding Multivariable Calculus: Problems, Solutions, and Tips, taught by award-winning Professor Bruce H. Edwards, is the next step for students and professionals to expand their knowledge for work or study in many quantitative fields, as well as an intellectual exercise for teachers, retired professionals, and anyone else who wants to understand the amazing applications of 3-D calculus. How does one control a robot whose motion depends on several variables at once? c) What about three planes in 3d space? *The sort of material in Stewart's . James Stewart's CALCULUS texts are world-wide best-sellers for a reason: they are clear, accurate, and filled with relevant, real-world examples. The module covered chapters 15, 16 and 17 of. Answer (1 of 5): The skills that allow someone to succeed in multivariable calculus and the skills that allow success in linear algebra seem to come from other 'sources' even though they're both inherently mathematical. Understanding Multivariable Calculus: Problems, Solutions, and Tips, taught by award-winning Professor Bruce H. Edwards of the University of Florida, is the next step for students and professionals to expand their knowledge for work or study in many quantitative fields, as well as an eye-opening intellectual exercise for teachers, retired . and Tips, a natural predecessor for this course, does introduce some topics in preparation for multivariable calculusconics, vectors, parametric equations, polar coordinates, and vector-valued functionsthe bulk of that courses is concerned with topics such as infinite series that are important for higher forms of mathematical analysis but . It's a rich subject with its own unique puzzles and surprises. Multivariable calculus: hard problems with solutions. Vector calculus and multivariable calculus sites: Georgia Tech Vector calculus home page: Lecture notes, plus extensive collection of . Multivariable Calculus is the tool of choice to shed light on complex relationships between 2, 3, or hundreds of variables simultaneously. The new ninth edition continues the tradition of providing an accessible . Understanding Multivariable Calculus: Problems, Solutions, and Tips, taught by award-winning Professor Bruce H. Edwards, is the next step for students and professionals to expand their knowledge for work or study in many quantitative fields, as well as an intellectual exercise for teachers, retired professionals, and anyone else who wants to understand the amazing applications of 3-D calculus. MULTIVARIABLE CALCULUS, Stewart continues to set the standard for the course while adding carefully revised content. In economics , for example, consumer choice over a variety of goods, and producer choice over various inputs to use and outputs to produce, are modeled with multivariate . Examples of 2D Parametric Curves (13 minutes) (Part of Section . PS: I'm aware that a somewhat similar question has been asked here . Click on the " Solution " link for each problem to go to the page containing the solution. About this course. Watch the following video lectures on material from Sections 9.1 and 10.7 and 10.5. 2 Dierential Calculus for Functions of Several Variables 1. Multivariable calculus studies functions with two or more variables. Multivariable calculus continues the story of calculus 1-2: Practice Problems 4, PDF It is the second semester in the freshman calculus sequence A youtube Calculus Workbook (Part II) Introduction to Complex Numbers Note: Desmos uses cookies to enable persistence when you are signed in Note: Desmos uses cookies to enable persistence when you are . extension will nd exercises and problems that provide the key ideas and intro-duce the notational difculties. This booklet contains the worksheets for Math 53, U.C. Note that some sections will have more problems than others and some will have more or less of a variety of problems. Countless people have relied on Anton to learn the difficult concepts of calculus. BC Calc is the most difficult math course that most high school even have available to their students, so even though colleges will typically compare you to other applicants from your school, having BC instead of Multi shouldn't . A lot of the things you cover in calc 3 will be all about doing the things you learned in calc 1 and 2 but in multiple dimensions. If you are unsure of any of the problems, post a question to the Campuswire Class Feed and ask! The change that most interests us happens in systems with more than one variable: weather depends on time of year and location on the Earth, economies have several sectors, important chemical reactions have many reactants and products. The problems are provided together with detailed solutions as well as 2D and 3D figures. -Will understanding of calculus. Calc I is derivatives and integrals. b) What about two planes in 3d space? Mathematics. Problem 2E. If you are unsure of any of the problems, post a question to the Campuswire Class Feed and ask! Briey, the goal of these notes is to develop the theory of differentiation in arbitrary dimensions with more mathematical ma-turity than a typical calculus class, with an eye towards more advanced math. Utterly trivial problems sit alongside ones requiring substantial thought More In addition to a collection of 10 problems there are also some selected additional problems from old exams and Calculus I With Review nal exams in the period 2000-2009 Exams/Quizzes The full step-by-step solution to problem in Calculus: Single and Multivariable were . My school splits it up a bit differently than most others. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics. It's calculus done the old-fashioned way - one problem at a time, one easy-to-follow step at a time, with problems ranging in difficulty from easy to challenging. Multivariate calculus is an intensely difficult subject, and the pressure to be good or even "naturally good" at math is very stressful. This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. In general people report that multivariable calculus is easier, but a lot of that has to do with the fact that people who struggle in single variable calculus don't go on to take it. Multivariable calculus is much more than just a repeat of single-variable calculus, however. These functions depend on two or more input variables to produce an output. . Two lines on the xy plane either intersect at a point or are parallel. This booklet contains the worksheets for Math 53, U.C. Take one of our many Multivariable Calculus practice tests for a run-through of commonly asked questions. Multivariate Calculus is used everywhere in Machine Learning projects. Course Outcomes. able problems that have one-variable counterparts. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic. Rogawski, Calculus - Multivariable [Solutions], 2nd Ed The most successful calculus book of its generation, Jon Rogawski's Calculus offers an ideal balance of formal precision and dedicated conceptual focus, helping students build strong computational skills while continually reinforcing the relevance of calculus to their future studies and . Language: en. So basically at my school Calc I is normal Calc I + half of Calc II, while Calc II is the second half of Calc II + Calc III. 8 yr. ago Civil Engineering. To use important theorems in vector calculus in practical problem. Having taught these three classes, retake calc 1 and 2. They're not difficult, but the concepts build on calc 1 and 2. Skim through Sections 10.7 and 10.5 of the book. Like all other math classes, it takes some discipline to work through homework problems. Success in your calculus course starts here! Multivariable calculus continues the story of calculus. Physical applications will be highlighted, including the use of integrals to compute the work done by a force field, or the flux caused by a velocity field. The first part includes multivariable calculus material. In order to study functions of many variables which is the goal of multivariable calculus we rst need to understand the underlying universe which hosts all of the forthcoming . Afxy sinxy 01 bfx y z z x y 114 Answer. Utterly trivial problems sit alongside ones requiring substantial thought More In addition to a collection of 10 problems there are also some selected additional problems from old exams and Calculus I With Review nal exams in the period 2000-2009 Exams/Quizzes The full step-by-step solution to problem in Calculus: Single and Multivariable were . able problems that have one-variable counterparts. Will taking Multivariable Calculus look better to colleges compared to AP Calculus BC as an Engineering Major? Objectives. It introduces new tools that solve important problems in machine learning, neural networks, engineering, quantum computing, and astrophysics, to name just a few. The questions emphasize qualitative issues and the problems are more computationally intensive. CO1. The process of reasoning by using mathematics is the primary objective of the course, and not simply being able to do computations. In my opinion, math courses are the easiest way to raise the science GPA. Variables are all around us: temperature, altitude, location, profit, color, and countless others. Multivariable calculus extends one variable calculus into situations where the do-main and/or the range of functions becomes multidimensional. Suppose that the level curves of a function z = f(x,y) consists of straight lines. We had a lot of multivariable calc and beginning differential equations in my Calc 2 class. This book covers the standard material for a one-semester course in multivariable calculus. . It is simply a place to start. Bonus points if the book discusses differentials. It wasn't hard when you get used to it. In this course students learn to differentiate and integrate functions of several variables. Difficult take on multivariable calculus as expected for a Princeton course. Differential Equations and Multivariable Calculus can be troublesome for many students. . Reeve Garrett In organizing this lecture note, I am indebted by Cedar Crest College Calculus IV Lecture Notes, Dr. James Hammer [1]. Vector calculus is a collection of techniques for dealing with functions in three variables that has use in physics and some branches of engineering. Math 213: Calculus I (4 credits) Math 214: Calculus II (4 credits) Math 351: Multivariable Calculus (4 credits) (same as Calculus III, Calculus IV, Vector Calculus) Math 317: Differential Equations (3 credits) Math 331: Linear Algebra (3 credits) Math 315: Probability Theory (3 credits) Calculus-Based Statistics. Problem 3E. As . In multivariable calculus we study functions of two or more independent variables, e.g., z=f(x, y)or w=f(x, y, z). Watch the following video lectures on material from Sections 9.1 and 10.7 and 10.5. The questions emphasize qualitative issues and the problems are more computationally intensive. Problem 1E. ";s:7:"keyword";s:33:"multivariable calculus difficulty";s:5:"links";s:1424:"<a href="https://www.mobilemotorcyclerepairnearme.org/rk72z8wr/fifa-switzerland-office">Fifa Switzerland Office</a>, <a href="https://www.mobilemotorcyclerepairnearme.org/rk72z8wr/forward-from-discord-to-telegram">Forward From Discord To Telegram</a>, <a href="https://www.mobilemotorcyclerepairnearme.org/rk72z8wr/punk-album-cover-inspiration">Punk Album Cover Inspiration</a>, <a href="https://www.mobilemotorcyclerepairnearme.org/rk72z8wr/luka-and-adrien-kiss-fanfiction">Luka And Adrien Kiss Fanfiction</a>, <a href="https://www.mobilemotorcyclerepairnearme.org/rk72z8wr/spots-where-you-might-count-sheep-nyt-crossword">Spots Where You Might Count Sheep Nyt Crossword</a>, <a href="https://www.mobilemotorcyclerepairnearme.org/rk72z8wr/cheap-things-to-do-on-big-island-hawaii">Cheap Things To Do On Big Island Hawaii</a>, <a href="https://www.mobilemotorcyclerepairnearme.org/rk72z8wr/chuckwalla-lifespan-in-captivity">Chuckwalla Lifespan In Captivity</a>, <a href="https://www.mobilemotorcyclerepairnearme.org/rk72z8wr/odgers-berndtsonexecutive-search-firm">Odgers Berndtsonexecutive Search Firm</a>, <a href="https://www.mobilemotorcyclerepairnearme.org/rk72z8wr/university-of-florida-women%27s-lacrosse-camp-2022">University Of Florida Women's Lacrosse Camp 2022</a>, <a href="https://www.mobilemotorcyclerepairnearme.org/rk72z8wr/kia-sportage-reverse-sensor-not-beeping">Kia Sportage Reverse Sensor Not Beeping</a>, ";s:7:"expired";i:-1;}
© 2017 -
ZeroByte.ID
.