Integral Calculus 2019 Fall

The material on this webspage accompanies the courses MATH 2414.013 and MATH 2414.014 at The University of Texas at Dallas.

Instructor: Dr. Yi Zhang

Syllabus: [doc]

Textbook:

Lecture Notes and Homework:

  • Vectors and the Geometry of Space
    • Three-Dimensional Coordinate Systems
    • Vectors
  • Techniques of Integration
    • Integration by Parts
    • Trigonometric Integrals
    • Trigonometric Substitution
    • Integration of Rational Functions by Partial Functions [pdf]
    • Strategy for Integration [pdf]
    • Improper Integrals [pdf]
  • Further Applications of Integration
  • Differential Equations
    • Modeling with Differential Equations [pdf]
    • Direction Fields and Euler's Method [pdf]
    • Review for Chapter 12, 7, and 8 [pdf]
    • Separable Equations [pdf]
    • Models for Population Growth [pdf]
    • Predator-Prey Systems [pdf]

    • Homework 2 [pdf]
  • Parametric Equations and Polar Coordinates
    • Curves Defined by Parametric Equations [pdf]
    • Calculus with Parametric Curves [pdf]
    • Polar Coordinates [pdf]
    • Areas and Lengths in Polar Coordinates [pdf]

    • Homework 3 [pdf]
  • Infinite Sequences and Series
    • Sequences [pdf]
    • Series [pdf]
    • The Integral Test and Estimates of Sums [pdf]
    • The Comparison Tests [pdf]
    • Alternating Series [pdf]
    • Absolute Convergence and the Ratio and Root Tests [pdf]
    • Strategy for Testing Series [pdf]
    • Power Series [pdf]
    • Representations of Functions as Power Series [pdf]
    • Taylor and Maclaurin Series [pdf]

    • Homework 4 [pdf]
    • Homework 5 [pdf]