University of Houston
Mathematics Department
MATH 1314: Elements of Calculus
Prerequisite: Credit for or placement out of Math 1310. Students with prior credit for Math 1431 will not be permitted to enroll in or receive credit for Math 1314.
Course Description: Curve sketching and graphical analysis, differentiation and integrations of elementary functions, topics in functions of several variables, applications in business and the social sciences.
Textbook: Text is in electronic form .
Course Policies ( pdf version )
| Chapter and Section | Suggested Exercises |
| Chapter 9 Pre-calculus Review (For review by student as needed) | |
| 9.1 Exponents and Radicals | |
| 9.2 Algebraic Expressions | |
| 9.3 Algebraic Fractions | |
| 9.4 Inequalities and Absolute Value | |
| CHAPTER 10 Functions, Limits and the Derivative | |
| 10.1 Functions and their Graphs | 5,7,9,33-52 |
| 10.2 The Algebra of Functions | Odds 1-23,25,29,30,31,34,39,47,48 |
| 10.3 Functions and the Mathematical Models in Calculus | 1-6,8,9,13,17 |
| 10.4 Limits | 1-8, odds 11-21, Odds 49-61 |
| 10.5 One-Sided Limits and Continuity | 1-8,21,23,27 |
| 10.6 The Derivative | Odds 9-15,17,19,23,27 |
| CHAPTER 11 Differentiation | |
| 11.1 Basic Rules of Differentiation | Odds 1-23 |
| 11.2 The Product and Quotient Rules | 1,7,11,13,17,23,27,29,31,37,41 |
| 11.3 The Chain Rule | 1,7,13,19,23,29,33,37,43 |
| 11.5 Higher-Order Derivatives | 1,7,13,19,29 |
| CHAPTER 12 Applications of the Derivative | |
| 12.1 Applications of the First Derivative | 1-8,11,15,21,27,33,Odds 37-43, 51,55,57,63,67,74 |
| 12.2 Applications of the Second Derivative | 1-8,9-12,17,23,31,37,41,Odds 61-73 |
| 12.3 Curve Sketching | 1-10,11,15,19,21,25,33 |
| 12.4 Optimization I | 1-8,13,17,23,31,33,37,40,42 |
| 12.5 Optimization II | 1,3,4,5,9,18,19 |
| CHAPTER 13 Exponential and Logarithmic Functions | |
| 13.1 Exponential Functions | Odds 1-19,21,26 |
| 13.2 Logarithmic Functions | Odds 17-25, Odds 33-39 |
| 13.3 Differentiation of Exponential Functions | 1,5,11,15,21,25,33,36,37,43 |
| 13.4 Differentiation of Logarithmic Functions | 1,7,11,13,19,29,33,47,50,53 |
| CHAPTER 14 Integration | |
| 14.1 Anti-derivatives and Rules of Integration | 9,13,17,21,25,31,35,39,43,47,49,51,55,63 |
| 14.2 Integration by SubstitutionAlternate | Odds 1-49 |
| 14.3 Area and the Definite Integral | 1,3,4 |
| 14.4 The Fundamental Theorem of Calculus | Alternate Odds 17-37 |
| 14.5 Evaluating Definite IntegralsAlternate | Odds 1-27 |
| 14.6 Area Between Two Curves | 7,11,19,25,31,34 |
| CHAPTER 15 Additional Topics in Integration | |
| 15.1 Integration by Parts | 1,5,11,15,19,23,26,27,29 |
| CHAPTER 16 Calculus of Several Variables | |
| 16.1 Functions of Several Variables | 7,13,17,21 |
| 16.2 Partial Derivatives | 1,5,9,13,17,21,23,30 |
| 16.3 Maxima and Minima of Functions of Several Variables | 1,5,9,20,27,29 |