This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.
Applied Calculus -- Spring 2015
From Mathematics Is A Science
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MTH 140 - Applied Calculus A brief survey of calculus including both differentiation and integration with applications. Not to be substituted for Mathematics 229. PR: ACT Math 24 or MTH127 or MTH130. 3 hours
- Time and Place: 1:00 - 1:50 pm MWR at 335 Smith Hall.
- Instructor: Peter Saveliev (call me Peter)
- Office: 713 Smith Hall
- Office Hours: MW 2:30-4:45 (walk-in), or by appointment
- Office Phone: x4639
- E-mail: saveliev@marshall.edu
- Class Web-Page: math01.com
- Prerequisites: excellent algebra skills, the ability to recognize and use functions, including the major classes of functions, graph these functions, solve equations -- College Algebra -- Fall 2014
- Text: Applied Calculus for the Life and Social Sciences by Larson
- Computer Restrictions: no better than graphic calculator TI-83 or TI-83+
- Outcomes: the student will learn to differentiate and integrate, apply these concepts and tools to study processes and patterns in physical and other sciences, become familiar with multivariable calculus.
- Activities: the student will practice each outcome via the homework given in the textbook and online.
- Evaluation: the student achievement of each outcome will be assessed via
- quizzes: taken from the textbook's exercise sets
- homework: accessed and graded online, provided by Webwork, http://webwork.marshall.edu/webwork2/S15-Math-140-Saveliev/
- tests: based on the textbook's exercises
- Grade Breakdown: TOTAL = .05×A + .40×(Q + H) + .20×M + .35×F
- attendance and participation: 5%
- quizzes and online homework: 40%
- midterm: 20%
- final exam: 35%
For details, see Course policy.
Mathematics Tutor Lab: Smith Music 115
Contents
1 Lectures
They will appear exactly as you see them in class and, as the course progresses, will be updated weekly.
2 Homework
Follow this link to access the online homework: Webwork
Assignments:
- Orientation (not for credit)
- Review
- Chapter1
- Chapter1b
- Chapter2
- Chapter2b
- Chapter2-3
- Chapter3
- Chapter3-4
- Chapter4-5-6
- Chapter7
- Chapter7b
- Chapter7c -- due Friday
3 Schedule
- Chapter 0. A Precalculus Review
- 0.1 The Real Number Line and Order
- 0.2 Absolute Value and Distance on the Real Number Line
- 0.3 Exponents and Radicals
- 0.4 Factoring Polynomials
- 0.5 Fractions and Rationalization
Week 1 -- 1/12
- Chapter 1. Functions, Graphs, and Limits
- 1.1 The Cartesian Plane and the Distance Formula
- 1.2 Graphs of Equations
- 1.3 Lines in the Plane and Slope
Week 2 -- 1/19
- 1.4 Functions
- 1.5 Limits
Week 3 -- 1/26
- 1.6 Continuity
- Chapter 2. Differentiation
- 2.1 The Derivative and the Slope of a Graph
Week 4 -- 2/2
- 2.2 Some Rules for Differentiation
- 2.3 Rates of Change
Week 5 -- 2/9
- 2.4 The Product and Quotient Rules
- 2.5 The Chain Rule
Week 6 -- 2/16
- 2.6 Higher-Order Derivatives
- Chapter 3. Applications of the Derivative
- 3.1 Increasing and Decreasing Functions
Week 7 -- 2/23
- 3.2 Extrema and the First-Derivative Test
- 3.3 Concavity and the Second-Derivative
- 3.4 Optimization Problems
- 3.6 Curve Sketching: A Summary
Week 8 -- 3/2
- Chapter 4. Exponential and Logarithmic Functions
- 4.1 Exponential Functions
- 4.2 Natural Exponential Functions
- 4.3 Derivatives of Exponential Functions
- 4.4 Logarithmic Functions
- 4.5 Derivatives of Logarithmic Functions
- 4.6 Exponential Growth and Decay
Week 9 -- 3/9
- Chapter 5. Trigonometric Functions
- 5.1 Radian Measure of Angles
- 5.2 The Trigonometric Functions
- 5.3 Graphs of Trigonometric Functions
- 5.4 Derivatives of Trigonometric Functions
Spring Break -- 3/16
Week 10 -- 3/23
- Chapter 6. Integration and Its Applications
- 6.1 Antiderivatives and Indefinite Integrals
- 6.3 Exponential and Logarithmic Integrals
- 6.4 Area and the Fundamental Theorem of Calculus
Week 11 -- 3/30
- Chapter 7. Techniques of Integration
- 7.3 Integrals of Trigonometric Functions
- 7.4 The Definite Integral as the Limit of a Sum
- 7.5 Numerical Integration
- 7.6 Improper Integrals
Week 12 -- 4/6
- Chapter 9. Functions of Several Variables
- 9.1 The Three-Dimensional Coordinate System
- 9.2 Surfaces in Space
Week 13 -- 4/13
- 9.3 Functions of Several Variables
Week 14 -- 4/20
- 9.4 Partial Derivatives
Week 15 -- 4/27
- 9.5 Extrema of Functions of Two Variables
- 9.7 Double Integrals and Area in the Plane
- Chapter 0. A Precalculus Review
- 0.1 The Real Number Line and Order
- 0.2 Absolute Value and Distance on the Real Number Line
- 0.3 Exponents and Radicals
- 0.4 Factoring Polynomials
- 0.5 Fractions and Rationalization
- Chapter 1. Functions, Graphs, and Limits
- 1.1 The Cartesian Plane and the Distance Formula
- 1.2 Graphs of Equations
- 1.3 Lines in the Plane and Slope
- 1.4 Functions
- 1.5 Limits
- 1.6 Continuity
- Chapter 2. Differentiation
- 2.1 The Derivative and the Slope of a Graph
- 2.2 Some Rules for Differentiation
- 2.3 Rates of Change
- 2.4 The Product and Quotient Rules
- 2.5 The Chain Rule
- 2.6 Higher-Order Derivatives
- Chapter 3. Applications of the Derivative
- 3.1 Increasing and Decreasing Functions
- 3.2 Extrema and the First-Derivative Test
- 3.3 Concavity and the Second-Derivative
- 3.4 Optimization Problems
- 3.5 Asymptotes
- 3.6 Curve Sketching: A Summary
- 3.7 Differentials: Linear Approximation
- Chapter 4. Exponential and Logarithmic Functions
- 4.1 Exponential Functions
- 4.2 Natural Exponential Functions
- 4.3 Derivatives of Exponential Functions
- 4.4 Logarithmic Functions
- 4.5 Derivatives of Logarithmic Functions
- 4.6 Exponential Growth and Decay
- Chapter 5. Trigonometric Functions
- 5.1 Radian Measure of Angles
- 5.2 The Trigonometric Functions
- 5.3 Graphs of Trigonometric Functions
- 5.4 Derivatives of Trigonometric Functions
- Chapter 6. Integration and Its Applications
- 6.1 Antiderivatives and Indefinite Integrals
- 6.2 Integration by Substitution and The General Power Rule
- 6.3 Exponential and Logarithmic Integrals
- 6.4 Area and the Fundamental Theorem of Calculus
- 6.5 The Area of a Region Bounded by Two Graphs
- 6.6 Volumes of Solids of Revolution
- Chapter 7. Techniques of Integration
- 7.1 Integration by Parts
- 7.2 Partial Fractions and Logistic Growth
- 7.3 Integrals of Trigonometric Functions
- 7.4 The Definite Integral as the Limit of a Sum
- 7.5 Numerical Integration
- 7.6 Improper Integrals
- Chapter 8. Matrices
- 8.1 Systems of Linear Equations in Two Variables
- 8.2 Systems of Linear Equations in More Than Two Variables
- 8.3 Matrices and Systems of Linear Equations
- 8.4 Operations with Matrices
- 8.5 The Inverse of a Matrix
- Chapter 9. Functions of Several Variables
- 9.1 The Three-Dimensional Coordinate System
- 9.2 Surfaces in Space
- 9.3 Functions of Several Variables
- 9.4 Partial Derivatives
- 9.5 Extrema of Functions of Two Variables
- 9.6 Least Squares Regression Analysis
- 9.7 Double Integrals and Area in the Plane
- 9.8 Applications of Double Integrals
- Chapter 10. Differential Equations
- 10.1 Solutions of Differential Equations
- 10.2 Separation of Variables
- 10.3 First-Order Linear Differential Equations
- 10.4 Applications of Differential Equations
- Chapter 11. Probability and Calculus
- 11.1 Discrete Probability
- 11.2 Continuous Random Variables
- 11.3 Expected Value and Variance
4 Exams
Upcoming:
- Applied Calculus -- Spring 2015 -- midterm, Monday March 9.
- Applied Calculus -- Spring 2015 -- final exam, Friday May 8, 12:45-2:45 pm, same place. Note: If the two-hour time allowance results in a conflict in exam times, it is the student’s responsibility to notify the professor of the later course and to reschedule the later exam.
Related old exams: