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# 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.

## Online Content

The Lumen OHM coursepack  provides a starting place for building a custom course. Algorithmic practice and assessment problem sets can be assimilated in the platform.