{"id":492,"date":"2017-09-08T10:22:17","date_gmt":"2017-09-08T09:22:17","guid":{"rendered":"http:\/\/salfordphysics.com\/?page_id=492"},"modified":"2023-09-21T10:05:26","modified_gmt":"2023-09-21T09:05:26","slug":"mathematics-hyper-tutorials","status":"publish","type":"page","link":"https:\/\/salfordphysics.com\/index.php\/mathematics-hyper-tutorials\/","title":{"rendered":"Mathematics Hyper-Tutorials"},"content":{"rendered":"

Contents – Background<\/a> | Vector Product Maths Tutorials<\/a> | Integration Maths Tutorials<\/a> | Ordinary Differential Equation Maths Tutorials<\/a> | Power Series and Fourier Series Maths Tutorials<\/a><\/p>\n

<\/a>Maths Tutorials – Background<\/h2>\n

Feel free to use and distribute these tutorials, keeping each intact. They were developed as part of the FDTL4 PPLATO<\/a> (Promoting Physics Learning And Teaching Opportunities) project, led by Dr Mike Tinker. Some of the tutorials are co-authored with Dr Silvia Dalla<\/a>. Click on any of the tutorials below to launch it. They are hyper-linked pdf files that use AcroTeX (by D.P. Story<\/a>).<\/p>\n

<\/a>Vector Product – Maths Tutorials<\/h2>\n

Scalar product of vectors<\/h3>\n

\"Scalar<\/a>
\nMaths tutorial – scalar product of vectors<\/a><\/p>\n

<\/a><\/p>\n

Vector product of vectors<\/h3>\n

\"Vector<\/a>
\nMaths tutorial – vector product of vectors<\/a><\/p>\n

<\/a>Integration – Maths Tutorials<\/h2>\n

Integration by substitution I<\/h3>\n

\"Integration<\/a>
\nIntegration by substitution – Tutorial 1<\/a><\/p>\n

Integration by substitution II<\/h3>\n

\"Integration<\/a>
\nIntegration by substitution – Tutorial 2<\/a><\/p>\n

Integration by substitution III<\/h3>\n

\"Integration<\/a>
\nIntegration by substitution – Tutorial 3<\/a><\/p>\n

<\/a><\/p>\n

Integration of algebraic fractions<\/h3>\n

\"Integration<\/a>
\nMaths tutorial – integration of algebraic fractions<\/a><\/p>\n

<\/a><\/p>\n

Integration using trig identities<\/h3>\n

\"Integration<\/a>
\nMaths tutorial – integration using trig identities<\/a><\/p>\n

<\/a><\/p>\n

Integration by parts<\/h3>\n

\"Integration<\/a>
\nMaths tutorial – integration by parts<\/a><\/p>\n

<\/a>Ordinary Differential Equation (ODE) – Maths Tutorials<\/h2>\n

ODE solution by direct integration<\/h3>\n

\"Ordinary<\/a>
\nMaths tutorial – direct integration (ODE’s)<\/a><\/p>\n

<\/a><\/p>\n

ODE solution by separation of variables<\/h3>\n

\"Ordinary<\/a>
\nMaths tutorial – separation of variables (ODE’s)<\/a><\/p>\n

<\/a><\/p>\n

Solution of ODE’s involving homogeneous functions<\/h3>\n

\"Ordinary<\/a>
\nMaths tutorial – homogeneous functions (ODE’s)<\/a><\/p>\n

<\/a><\/p>\n

ODE solution by integrating factor method<\/h3>\n

\"Ordinary<\/a>
\nMaths tutorial – integrating factor method (ODE’s)<\/a><\/p>\n

<\/a><\/p>\n

Bernoulli differential equations<\/h3>\n

\"Bernoulli<\/a>
\nMaths tutorial – Bernoulli differential equations<\/a><\/p>\n

<\/a><\/p>\n

Exact differential equations<\/h3>\n

\"Exact<\/a>
\nMaths tutorial – exact differential equations<\/a><\/p>\n

<\/a><\/p>\n

Second order differential equations I<\/h3>\n

\"Second<\/a>
\nMaths tutorial – second order, RHS=0 (ODE’s)<\/a><\/p>\n

Second order differential equations II<\/h3>\n

\"Second<\/a>
\nMaths tutorial – second order, RHS not 0 (ODE’s)<\/a><\/p>\n

<\/a>Power Series and Fourier Series – Maths Tutorials<\/h2>\n

Power series tutorial<\/h3>\n

\"Power<\/a>
\nMaths tutorial – using power series<\/a><\/p>\n

<\/a><\/p>\n

Fourier series tutorial<\/h3>\n

\"Fourier<\/a>
\nMaths tutorial – using Fourier series<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Contents – Background | Vector Product Maths Tutorials | Integration Maths Tutorials | Ordinary Differential Equation Maths Tutorials | Power Series and Fourier Series Maths Tutorials Maths Tutorials – Background Feel free to use and distribute these tutorials, keeping each intact. They were developed as part of the FDTL4 PPLATO (Promoting Physics Learning And Teaching … Continue reading Mathematics Hyper-Tutorials<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-492","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/salfordphysics.com\/index.php\/wp-json\/wp\/v2\/pages\/492","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/salfordphysics.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/salfordphysics.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/salfordphysics.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/salfordphysics.com\/index.php\/wp-json\/wp\/v2\/comments?post=492"}],"version-history":[{"count":3,"href":"https:\/\/salfordphysics.com\/index.php\/wp-json\/wp\/v2\/pages\/492\/revisions"}],"predecessor-version":[{"id":2336,"href":"https:\/\/salfordphysics.com\/index.php\/wp-json\/wp\/v2\/pages\/492\/revisions\/2336"}],"wp:attachment":[{"href":"https:\/\/salfordphysics.com\/index.php\/wp-json\/wp\/v2\/media?parent=492"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}