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Study Guides > Calculus 1 and 2

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.
Course Home Page
Content Block with Text, Assessments and Video links.

Course Review Access

Follow the link to review the Calculus 1 and 2 course materials in Lumen OHM.