This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.
Applied Calculus -- Spring 2015
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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
Lectures
They will appear exactly as you see them in class and, as the course progresses, will be updated weekly.
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
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
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: