Text<\/h3>\r\nThis course for Calculus 1 and 2 is based on Contemporary Calculus ![](\"https:\/\/www.myopenmath.com\/img\/extlink.png\")
<\/a> by Dale Hoffman. \u00a0A printed version of the calculus 1 (ch. 1-4) book is available on Amazon <\/a>. \u00a0A printed version of the Calculus 2 (ch. 5-10) book is available on Lulu <\/a> (soon to be on Amazon). \u00a0 The PDFs for chapters 1-3 in this course shell are reformatted versions of the original text which are not yet complete, and will not match the page numbers of the original text.\r\nTopic Overview<\/h3>\r\nThis course is delivered in 15 chapters including the following topics:\r\n\r\nChapter 0 -- Review and Preview<\/b>\r\n\r\n \t- \u00a0Lines<\/li>\r\n \t
- Functions<\/li>\r\n \t
- Combinations of functions<\/li>\r\n \t
- Mathematical language<\/li>\r\n<\/ul>\r\nChapter 1 --\u00a0Functions, Graphs, Limits, and Continuity<\/b>\r\n
\r\n \t- Sopes & velocity<\/li>\r\n \t
- Limit of a function,\u00a0limit properties, formal definition of limits<\/li>\r\n \t
- Continuous functions<\/li>\r\n<\/ul>\r\nChapter 2 --\u00a0The Derivative<\/b>\r\n
\r\n \t- Slope of a tangent line<\/li>\r\n \t
- Definition of a derivative, differentiation formulas, chain rule, related rates<\/li>\r\n \t
- Newton's method, linear approximation, implicit differentiation<\/li>\r\n<\/ul>\r\nChapter 3 -- Derivatives and Graphs<\/b>\r\n
\r\n \t- Max\/ Min, applied max and min., \u00a0mean value theorem<\/li>\r\n \t
- Graphs of derivatives of functions<\/li>\r\n \t
- Asymptotes, L'Hopital's rule<\/li>\r\n<\/ul>\r\nChapter 4 -- The integral<\/b>\r\n
\r\n \t- Sigma notation and Reimann sums<\/li>\r\n \t
- Definite integrals and their properties, areas and antiderivatives<\/li>\r\n \t
- Applications and approximations of definite integrals<\/li>\r\n<\/ul>\r\nChapter 5 --\u00a0Applications of Definite Integrals<\/b>\r\n
\r\n \t- Volume, arc length, surface area<\/li>\r\n \t
- Work, moments and centers of mass<\/li>\r\n<\/ul>\r\nChapter 6 --\u00a0Introduction to Differential Equations<\/b>\r\n
\r\n \t- Separable differential equations<\/li>\r\n \t
- Exponential growth, decay, and cooling<\/li>\r\n<\/ul>\r\nChapter 7 -- Inverse Trigonometric Functions<\/b>\r\n
\r\n \t- Transcendental functions, calculus with inverse trig functions<\/li>\r\n<\/ul>\r\nChapter 8 --\u00a0Improper Integrals and Integration Techniques<\/b>\r\n
\r\n \t- Improper integrals<\/li>\r\n \t
- Integration by parts, partial fraction decomposition, trig substitution<\/li>\r\n<\/ul>\r\nChapter 9 --\u00a0Polar, Parametric & Conics<\/b>\r\n
\r\n \t- Polar coordinates, calculus with polar coordinates<\/li>\r\n \t
- Parametric equations, calculus with parametric equations<\/li>\r\n \t
- Bezier curves, conic sections, properties of conic sections<\/li>\r\n<\/ul>\r\nChapter 10 --\u00a0Infinite Series and Power Series<\/b>\r\n
\r\n \t- Geometric and harmonic series, alternating sign series, power series, Taylor and Macalurin series<\/li>\r\n \t
- Tests for convergence<\/li>\r\n \t
- Approximation with Taylor Polynomials<\/li>\r\n<\/ul>\r\nChapter 11 --\u00a0Vectors, Lines, and Planes in 3D<\/b>\r\n
\r\n \t- Vectors in the plane<\/li>\r\n \t
- Rectangular coordinates in 3D, vectors in 3D, lines and planes in 3D<\/li>\r\n<\/ul>\r\nChapter 12 --\u00a0Vector Valued Functions<\/b>\r\n
\r\n \t- Derivatives, curves in space<\/li>\r\n \t
- Cylindrical and spherical coordinates in 3D<\/li>\r\n<\/ul>\r\nChapter 13 --\u00a0Functions of Several Variables<\/b>\r\n
\r\n \t- Limits, partial derivatives, tangent planes and differentials<\/li>\r\n \t
- Gradients, max\/ min<\/li>\r\n \t
- Lagrange multipliers<\/li>\r\n<\/ul>\r\nChapter 14 --\u00a0Double and Triple Integrals<\/b>\r\n
\r\n \t- Over rectangular domains, in polar coordinates<\/li>\r\n \t
- Applications of double integrals<\/li>\r\n \t
- Surface area<\/li>\r\n \t
- Triple integrals<\/li>\r\n \t
- Change of variables<\/li>\r\n<\/ul>\r\nChapter 15 --\u00a0Vector Calculus<\/b>\r\n
\r\n \t- Vector fields, divergence, curl, line integrals, potential functions<\/li>\r\n \t
- Green's theorem, Stokes and Gauss' equations<\/li>\r\n<\/ul>\r\nLength: <\/strong>Two\u00a0semesters, three quarters\r\n\r\nDelivery: <\/strong>This course contains content that could be delivered as an online course (although why you would want to take Calculus online, I don't know...), or face to face.\r\n
Online Content<\/h2>\r\nThe Lumen OHM coursepack \u00a0provides\u00a0a starting place for building a custom course.\r\n\r\nAlgorithmic practice and assessment problem sets can be assimilated in the platform.\r\nCourse Home Page<\/strong>\r\n![\"Screen](\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/270\/2016\/10\/25215830\/Screen-Shot-2016-10-25-at-2.57.44-PM-300x240.png\")
<\/a><\/div>\r\nContent Block with Text, Assessments\u00a0and Video links.<\/strong>\r\n<\/a>![\"Screen](\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/270\/2016\/10\/25220015\/Screen-Shot-2016-10-25-at-2.59.41-PM-300x141.png\")
<\/a><\/div>\r\nCourse Review Access<\/h2>\r\nFollow the link to review the\u00a0Calculus 1 and 2 course materials in Lumen OHM.\u00a0<\/a>\r\n<\/div>","rendered":"Content Overview<\/h2>\n
- \r\n \t
- \u00a0Lines<\/li>\r\n \t
- Functions<\/li>\r\n \t
- Combinations of functions<\/li>\r\n \t
- Mathematical language<\/li>\r\n<\/ul>\r\nChapter 1 --\u00a0Functions, Graphs, Limits, and Continuity<\/b>\r\n
- \r\n \t
- Sopes & velocity<\/li>\r\n \t
- Limit of a function,\u00a0limit properties, formal definition of limits<\/li>\r\n \t
- Continuous functions<\/li>\r\n<\/ul>\r\nChapter 2 --\u00a0The Derivative<\/b>\r\n
- \r\n \t
- Slope of a tangent line<\/li>\r\n \t
- Definition of a derivative, differentiation formulas, chain rule, related rates<\/li>\r\n \t
- Newton's method, linear approximation, implicit differentiation<\/li>\r\n<\/ul>\r\nChapter 3 -- Derivatives and Graphs<\/b>\r\n
- \r\n \t
- Max\/ Min, applied max and min., \u00a0mean value theorem<\/li>\r\n \t
- Graphs of derivatives of functions<\/li>\r\n \t
- Asymptotes, L'Hopital's rule<\/li>\r\n<\/ul>\r\nChapter 4 -- The integral<\/b>\r\n
- \r\n \t
- Sigma notation and Reimann sums<\/li>\r\n \t
- Definite integrals and their properties, areas and antiderivatives<\/li>\r\n \t
- Applications and approximations of definite integrals<\/li>\r\n<\/ul>\r\nChapter 5 --\u00a0Applications of Definite Integrals<\/b>\r\n
- \r\n \t
- Volume, arc length, surface area<\/li>\r\n \t
- Work, moments and centers of mass<\/li>\r\n<\/ul>\r\nChapter 6 --\u00a0Introduction to Differential Equations<\/b>\r\n
- \r\n \t
- Separable differential equations<\/li>\r\n \t
- Exponential growth, decay, and cooling<\/li>\r\n<\/ul>\r\nChapter 7 -- Inverse Trigonometric Functions<\/b>\r\n
- \r\n \t
- Transcendental functions, calculus with inverse trig functions<\/li>\r\n<\/ul>\r\nChapter 8 --\u00a0Improper Integrals and Integration Techniques<\/b>\r\n
- \r\n \t
- Improper integrals<\/li>\r\n \t
- Integration by parts, partial fraction decomposition, trig substitution<\/li>\r\n<\/ul>\r\nChapter 9 --\u00a0Polar, Parametric & Conics<\/b>\r\n
- \r\n \t
- Polar coordinates, calculus with polar coordinates<\/li>\r\n \t
- Parametric equations, calculus with parametric equations<\/li>\r\n \t
- Bezier curves, conic sections, properties of conic sections<\/li>\r\n<\/ul>\r\nChapter 10 --\u00a0Infinite Series and Power Series<\/b>\r\n
- \r\n \t
- Geometric and harmonic series, alternating sign series, power series, Taylor and Macalurin series<\/li>\r\n \t
- Tests for convergence<\/li>\r\n \t
- Approximation with Taylor Polynomials<\/li>\r\n<\/ul>\r\nChapter 11 --\u00a0Vectors, Lines, and Planes in 3D<\/b>\r\n
- \r\n \t
- Vectors in the plane<\/li>\r\n \t
- Rectangular coordinates in 3D, vectors in 3D, lines and planes in 3D<\/li>\r\n<\/ul>\r\nChapter 12 --\u00a0Vector Valued Functions<\/b>\r\n
- \r\n \t
- Derivatives, curves in space<\/li>\r\n \t
- Cylindrical and spherical coordinates in 3D<\/li>\r\n<\/ul>\r\nChapter 13 --\u00a0Functions of Several Variables<\/b>\r\n
- \r\n \t
- Limits, partial derivatives, tangent planes and differentials<\/li>\r\n \t
- Gradients, max\/ min<\/li>\r\n \t
- Lagrange multipliers<\/li>\r\n<\/ul>\r\nChapter 14 --\u00a0Double and Triple Integrals<\/b>\r\n
- \r\n \t
- Over rectangular domains, in polar coordinates<\/li>\r\n \t
- Applications of double integrals<\/li>\r\n \t
- Surface area<\/li>\r\n \t
- Triple integrals<\/li>\r\n \t
- Change of variables<\/li>\r\n<\/ul>\r\nChapter 15 --\u00a0Vector Calculus<\/b>\r\n
- \r\n \t
- Vector fields, divergence, curl, line integrals, potential functions<\/li>\r\n \t
- Green's theorem, Stokes and Gauss' equations<\/li>\r\n<\/ul>\r\nLength: <\/strong>Two\u00a0semesters, three quarters\r\n\r\nDelivery: <\/strong>This course contains content that could be delivered as an online course (although why you would want to take Calculus online, I don't know...), or face to face.\r\n
Online Content<\/h2>\r\nThe Lumen OHM coursepack \u00a0provides\u00a0a starting place for building a custom course.\r\n\r\nAlgorithmic practice and assessment problem sets can be assimilated in the platform.\r\n
Course Home Page<\/strong>\r\n<\/a><\/div>\r\nContent Block with Text, Assessments\u00a0and Video links.<\/strong>\r\n<\/a><\/a><\/div>\r\nCourse Review Access<\/h2>\r\nFollow the link to review the\u00a0Calculus 1 and 2 course materials in Lumen OHM.\u00a0<\/a>\r\n
<\/div>","rendered":"Content Overview<\/h2>\n
- Transcendental functions, calculus with inverse trig functions<\/li>\r\n<\/ul>\r\nChapter 8 --\u00a0Improper Integrals and Integration Techniques<\/b>\r\n
![\r\n<\/a>](\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/264\/2016\/10\/04014833\/Screen-Shot-2016-10-03-at-6.46.31-PM.png\"){kind=link}