# 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 |

**Course Description**: This course is delivered in Lumen OHM with automated grading of numerical and algebraic answers, similar to WebAssign and MyMathLab. This makes it appropriate for self-study by students, or as a face to face course. This course can be imported into your LMS (Blackboard, Canvas, Moodle) to provide a single-sign on experience for your students, as well as grade return for you.

### Text

This course for Calculus 1 and 2 is based on Contemporary Calculus by Dale Hoffman. A printed version of the calculus 1 (ch. 1-4) book is available on Amazon . A printed version of the Calculus 2 (ch. 5-10) book is available on Lulu (soon to be on Amazon). 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.### 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

**Chapter 1 -- Functions, Graphs, Limits, and Continuity**

- Sopes & velocity
- Limit of a function, limit properties, formal definition of limits
- Continuous functions

**Chapter 2 -- The Derivative**

- Slope of a tangent line
- Definition of a derivative, differentiation formulas, chain rule, related rates
- Newton's method, linear approximation, implicit differentiation

**Chapter 3 -- Derivatives and Graphs**

- Max/ Min, applied max and min., mean value theorem
- Graphs of derivatives of functions
- Asymptotes, L'Hopital's rule

**Chapter 4 -- The integral**

- Sigma notation and Reimann sums
- Definite integrals and their properties, areas and antiderivatives
- Applications and approximations of definite integrals

**Chapter 5 -- Applications of Definite Integrals**

- Volume, arc length, surface area
- Work, moments and centers of mass

**Chapter 6 -- Introduction to Differential Equations**

- Separable differential equations
- Exponential growth, decay, and cooling

**Chapter 7 -- Inverse Trigonometric Functions**

- Transcendental functions, calculus with inverse trig functions

**Chapter 8 -- Improper Integrals and Integration Techniques**

- Improper integrals
- Integration by parts, partial fraction decomposition, trig substitution

**Chapter 9 -- Polar, Parametric & Conics**

- Polar coordinates, calculus with polar coordinates
- Parametric equations, calculus with parametric equations
- Bezier curves, conic sections, properties of conic sections

**Chapter 10 -- Infinite Series and Power Series**

- Geometric and harmonic series, alternating sign series, power series, Taylor and Macalurin series
- Tests for convergence
- Approximation with Taylor Polynomials

**Chapter 11 -- Vectors, Lines, and Planes in 3D**

- Vectors in the plane
- Rectangular coordinates in 3D, vectors in 3D, lines and planes in 3D

**Chapter 12 -- Vector Valued Functions**

- Derivatives, curves in space
- Cylindrical and spherical coordinates in 3D

**Chapter 13 -- Functions of Several Variables**

- Limits, partial derivatives, tangent planes and differentials
- Gradients, max/ min
- Lagrange multipliers

**Chapter 14 -- Double and Triple Integrals**

- Over rectangular domains, in polar coordinates
- Applications of double integrals
- Surface area
- Triple integrals
- Change of variables

**Chapter 15 -- Vector Calculus**

- Vector fields, divergence, curl, line integrals, potential functions
- Green's theorem, Stokes and Gauss' equations

**Length:**Two semesters, three quarters

**Delivery:**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.