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MATH 255 Syllabus

Calculus II

Revised: September  2022

Course Description

Derivatives and integrals of transcendental functions, techniques of integration, indeterminant forms, improper integrals, infinite series. Prerequisite: Math 153. Four semester hours.

Student Learning Objectives

By the end of the course, the student will be able to:

  • Calculate areas between curves.
  • Compute volumes of solids by disks, washers, and cylindrical shells.
  • Compute arc-length of a curve and surface area.
  • Solve applied problems involving force and work.
  • Evaluate anti-derivatives and definite integrals using u-substitution, integration by parts, trigonometric substitution, partial fractions, completing the square, and appropriate use of technology.
  • Use simple approximation techniques for definite integrals, check the error bounds for each technique, and compare the strengths and weaknesses of each.
  • Evaluate improper integrals.
  • Compute areas of planar regions and arc-lengths of curves using polar coordinates.
  • Determine whether a sequence converges or diverges.
  • Determine whether a series converges conditionally, converges absolutely, or diverges using the appropriate methods, such as geometric series test, p-series test, the comparison test, the limit comparison test, the integral test, the ratio test, the root test, and the alternating series test.
  • Determine the radius of convergence and the interval of convergence of a power series.
  • Compute the Taylor and Maclaurin series of a function.

Text

Gilbert Strang, Edwin Herman, et al., Calculus, Volume 2, OpenStax, 2016

Grading Procedure

Grading procedures and factors influencing course grade are left to the discretion
of individual instructors, subject to general university policy.

Attendance Policy

Attendance policy is left to the discretion of individual instructors, subject to
general university policy.

Course Outline

Chapter 1: Integration (this chapter is review from Calculus I and should not occupy more than a week of class)
Section 1.1: Approximating Areas (optional)
Section 1.2: The Definite Integral (optional)
Section 1.3: The Fundamental Theorem of Calculus (optional)
Section 1.4: Integration Formulas and the Net Change Theorem (optional)
Section 1.5: Substitution (optional)
Section 1.6: Integrals Involving Exponential and Logarithmic Functions (optional)
Section 1.7: Integrals Resulting in Inverse Trigonometric Functions (optional)

Chapter 2: Applications of Integration (~3 weeks)
Section 2.1: Areas Between Curves
Section 2.2: Determining Volumes by Slicing
Section 2.3: Volumes of Revolution: Cylindrical Shells
Section 2.4: Arc Length of a Curve and Surface Area
Section 2.5: Physical Applications (optional)
Section 2.6: Moments and Centers of Mass (optional)
Section 2.7: Integrals, Exponential Functions, and Logarithms (optional 鈥� most material covered in other sections)
Section 2.8: Exponential Growth and Decay (optional)
Section 2.9: Calculus of the Hyperbolic Functions (optional)

Chapter 3: Techniques of Integration (~3.5 weeks)
Section 3.1: Integration by Parts
Section 3.2 Trigonometric Integrals
Section 3.3: Trigonometric Substitution
Section 3.4: Partial Fractions
Section 3.5 Other Strategies for Integration (optional)
Section 3.6: Numerical Integration (optional)
Section 3.7: Improper Integrals

Chapter 5: Sequences and Series (~3 weeks)
Section 5.1: Sequences
Section 5.2: Infinite Series
Section 5.3: The Divergence and Integral Tests
Section 5.4: Comparison Tests
Section 5.5: Alternating Series
Section 5.6: Ratio and Root Tests

Chapter 6: Power Series (~1.5 weeks)
Section 6.1: Power Series and Functions
Section 6.2: Properties of Power Series
Section 6.3: Taylor and Maclaurin Series
Section 6.4: Working with Taylor Series (optional 鈥� covered in discussion of previous section)

Chapter 7: Parametric Equations and Polar Coordinates (~2 weeks)
Section 7.1: Parametric Equations
Section 7.2: Calculus of Parametric Curves
Section 7.3: Polar Coordinates
Section 7.4: Area and Arc Length in Polar Coordinates
Section 7.5: Conic Sections (optional)

Additional sections may be covered, if time permits, at the instructor鈥檚 discretion.