# Math 126 syllabus

Calculus II

Course Description:  This course is a continuation of MA 125 with emphasis on integral calculus. Topics include techniques of integration; applications of the definite integral to geometry, natural sciences, engineering, and economics; improper integrals; infinite sequences and series; Taylor polynomials and Taylor series; parametric equations and polar coordinates. Core Course.
Prerequisites:  C or better in MA 125

Textbook:   Joel Hass and Maurice D. Weir: University Calculus - Early Transcendentals, Pearson, 4th edition, 2020

Coverage: Chapter 5 (5.5, 5.6), Chapter 6 (6.1-6.5), Chapter 7 (7.1, 7.3), Chapter 8 (8.1-8.4, 8.7), Chapter 9 (9.1-9.9), Chapter 10 (10.1-10.3, 10.5)

Calculator: A TI-30XIIS calculator is permitted to be used in this course.

Common Homework: Common homework is available through MyLabsPlus.

Learning outcomes: Upon the successful completion of the course a student will:
Apply Substitution Methods to Evaluate Integrals
Calculate the Integral of Products of Functions Using Integration by Parts
Compute Integrals which come out to Logarithmic and Inverse Trigonometric Functions
Calculate the Integral of Powers of Trigonometric Functions
Apply Trigonometric Substitution to Evaluate Integrals Involving Radicals
Calculate the Integral of Rational Functions Using the Method of Partial Fractions
Interpret the Area Between Two or More Curves as an Integral
Interpret the Volume of a Solid of Revolution as an Integral
Interpret the Length of a Curve as an Integral
Compute the Limit of a Sequence
Compute the Value of an Infinite Series Using Partial Sums
Evaluate Definite Integrals Over Infinite Intervals
Apply the Integral Test to Argue For or Against the Convergence of an Infinite Series
Apply Comparison Tests to Argue For or Against the Convergence of an Infinite Series
Classify Alternating Infinite Series as Absolutely Convergent, Conditionally Convergent, or Divergent
Apply the Ratio and Root Tests to Determine if an Infinite Series Converges Absolutely
Determine the Interval on Which a Power Series Converges
Compute the Taylor/Maclaurin Series of an Analytic Function and Determine the Interval of Convergence

Secondary Learning Outcomes:

Compute Derivatives and Integrals of Hyperbolic Trigonometric Functions and Inverse Hyperbolic Trigonometric Functions
Sketch the Graph of a Curve Given in Polar Coordinates
Interpret the Area of a Region Given in Polar Coordinates as an Integral
Sketch the Graph of a Curve Given in Parametric Coordinates
Compute the First and Second Spatial Derivatives of a Curve Given in Parametric Coordinates
Interpret the Surface Area of a Surface of Revolution as an Integral
Approximate Infinite Series Using Integrals
Approximate Alternating Series
Compute the Error Associated to a Given Taylor Polynomial Approximation
Apply Taylor Polynomials to Generate Approximations
Learning Outcomes for Quantitative Reasoning:
Convert relevant information into various mathematical forms (e.g., equations, graphs, diagrams, tables, words).
Solve mathematical problems.