Calculus I & II - Dale Hoffman
Content Overview
Course Materials | YES | NO |
Lumen OHM Questions? | X - for chapters 1-5, 7-15 | |
Editable Text? | X - access here | |
Video Support? | X - for CH. 1-5, 7-15 | |
Written Assessments/ Test? | X - practice sets with answers to odds | |
Workbook? | X |
Text
This course for Calculus 1 and 2 is based on Contemporary Calculus![](https://www.myopenmath.com/img/extlink.png)
![](https://www.myopenmath.com/img/extlink.png)
![](https://www.myopenmath.com/img/extlink.png)
Topic Overview
This course is delivered in 15 chapters including the following topics: Chapter 0 -- Review and Preview- Lines
- Functions
- Combinations of functions
- Mathematical language
- Sopes & velocity
- Limit of a function, limit properties, formal definition of limits
- Continuous functions
- Slope of a tangent line
- Definition of a derivative, differentiation formulas, chain rule, related rates
- Newton's method, linear approximation, implicit differentiation
- Max/ Min, applied max and min., mean value theorem
- Graphs of derivatives of functions
- Asymptotes, L'Hopital's rule
- Sigma notation and Reimann sums
- Definite integrals and their properties, areas and antiderivatives
- Applications and approximations of definite integrals
- Volume, arc length, surface area
- Work, moments and centers of mass
- Separable differential equations
- Exponential growth, decay, and cooling
- Transcendental functions, calculus with inverse trig functions
- Improper integrals
- Integration by parts, partial fraction decomposition, trig substitution
- Polar coordinates, calculus with polar coordinates
- Parametric equations, calculus with parametric equations
- Bezier curves, conic sections, properties of conic sections
- Geometric and harmonic series, alternating sign series, power series, Taylor and Macalurin series
- Tests for convergence
- Approximation with Taylor Polynomials
- Vectors in the plane
- Rectangular coordinates in 3D, vectors in 3D, lines and planes in 3D
- Derivatives, curves in space
- Cylindrical and spherical coordinates in 3D
- Limits, partial derivatives, tangent planes and differentials
- Gradients, max/ min
- Lagrange multipliers
- Over rectangular domains, in polar coordinates
- Applications of double integrals
- Surface area
- Triple integrals
- Change of variables
- Vector fields, divergence, curl, line integrals, potential functions
- Green's theorem, Stokes and Gauss' equations