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.
Textbook:
- James Stewart, Calculus, Early Transcendentals, 8th Edition. ISBN-13: 978-1285741550
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]