Calculus I

CVCC Course number - MTH 173 - 4 credit hours
INSTRUCTOR: Mr. Howard        ROOM: 205
TIME: MWTh  7:30 - 8:20, 8:25 – 9:20

COURSE DESCRIPTION: A college level study of differential calculus, this course includes the study of limits, continuity, derivatives (concept and definition), derivatives of parametric equations and polar curves,  differentiation techniques (including inverse trigonometric functions), curve sketching, optimization applications and an introduction to antiderivatives and definite integrals with applications.  Upon completion of the course the students earn 4 semester hours from the Central Virginia Community College.

 
COURSE CONTENT: 
 
At the end of the semester, the student will be able to: 
  • perform calculus operations, graph functions and solve equations using Derive
  • manipulate and graph numerical data using Excel
  • define a function and find domain and range
  • manipulate and develop mathematical models using the following functions: linear, exponential, power, inverse, logarithmic, trigonometric, polynomial and rational
  • transform functions and generate composite functions 
  • explain the concept of and evaluate limits 
  • find intervals of continuity for a function 
  • ‘construct’ the definition of the derivative 
  • explain how the secant and tangent line relate to the derivative, average and instantaneous rates of change, velocity and acceleration 
  • find approximations for the derivatives at a point 
  • use local linearity to estimate functional values 
  • apply appropriate techniques of differentiation (product, quotient, chain, exponential, logarithmic) 
  • differentiate trigonometric functions 
  • perform implicit differentiation 
  • solve related rates applications 
  • determine increasing and decreasing intervals of a function 
  • determine concavity of a function and points of inflection 
  • sketch curves using appropriate techniques 
  • solve optimization problems 
  • apply Newton 's method when finding roots 
  • recognize an antiderivative 
  • setup and evaluate Riemann Sums
  • evaluate definite integrals 

 

  Tentative Schedule:

 - Links to online documents and assignments are listed in blue.

Chapter 2

Week of ... Monday Wednesday Thursday  
8/15/11 Course Introduction
Sec 2.1
Secant and Tangent Lines		 Sec 2.1
Secant and Tangent Lines		 Sec. 2.2
The Limit - graphically and numerically
delta-epsilon definition		  
8/22/11 Sec 2.3
The Limit - Analytically		 Sec 2.4
Continuity
Intermediate Value Theorem

Sec 2.5
Limits involving Infinity

  
8/29/11 Q & A Day for Test #1 Test #1

 

  

Chapter 2 Homework Assignments

Sec 2.1    page 67: 1-3, 7, 8

Sec 2.2    page 74: 1, 5, 7, 9, 11, 14, 17, 23, 28, 33, 35, 38, 39, 49

Sec 2.3    page 87: 3, 7, 11, 21, 35, 37, 41, 43, 51-61 odd, 62, 69, 79, 80, 83, 109, 110

Sec 2.4    page 98: 3-6, 7-21 odd, 41-55 odd, 56, 63, 87, 90, 94

Sec 2.5    page 108: 9-17 odd, 33-38, 64, 67,

Applets for Chapter 2 topics

Continuity and Limits

  1. An Informal, Graphical View of Continuity
  2. Intermediate Value Theorem
  3. Informal View of Limits
  4. One- and Two-Sided Limits and When Limits Fail to Exist
  5. Limits at Infinity
  6. Table View of Limits
  7. Formal Definition of Limits
  8. Definition of Continuity Using Limits

 

Chapter 3

Week of ... Monday Wednesday Thursday
8/29/11     Sec 3.1
Definition of the derivative
Tangent Line
9/5/11 Labor Day - CVGS Closed Sec 3.2
Basic differentiation rules and properties		 Sec 3.2
Basic differentiation rules and properties
9/12/11 Sec 3.3
Product and Quotient Rules		 Sec 3.4
Chain Rule		 Q & A Day
9/19/11 Sec 3.5
Implicit Differentiation
Logarithmic differentiation		 Sec 3.5 cont
Implicit Differentiation
Logarithmic differentiation

Sec 3.6
Derivative of inverse functions
9/26/11 Sec 3.7
Related Rates		 Sec 3.7
Related Rates

Sec 3.8
Newton's Method
10/3/11 Teacher Work day Q & A Day Test #2

Chapter 3 Homework Assignments

Sec 3.1 page 123: 4, 7-23 odd, 37-40, 81-86

Sec 3.2 page 136: 3-23 odd, 39-51 odd, 57-61, 93, 95 97-100, 105, 108

Sec 3.3 page 147: 1-11 odd, 27, 31, 35, 41-57 odd, 77, 79, 91-93

Sec 3.4 Page 161: 9-35 odd, 55-75 odd, 159, 161, 169

Sec 3.5 Page 170: 1-19 odd, 31-37 odd, 40, 42, 45, 75, 87, 88

Sec 3.6 Page 179: 7, 9, 19-30, 65, 69, 71

Sec 3.7 Page 187: 3, 15, 19-24, 30-33, 35, 39, 48

Sec 3.8 Page 195: 5, 9, 15, 19, 21, 23, 47

Applets for Chapter 3 topics

Introduction to the Derivative

  1. Average Velocity and Speed
  2. Instantaneous Velocity
  3. Derivative at a Point
  4. Derivative Function
  5. A Tabular View of the Derivative
  6. Second Derivative
  7. A Tabular View of the Second Derivative
  8. Differentiability
  9. Twice Differentiable
  10. Making a Piecewise Function Continuous and Differentiable

Differentiation Short Cuts

  1. Constant, Line, and Power Functions
  2. Exponential Functions
  3. Trigonometric Functions
  4. Constant Multiple
  5. Combinations: Sum, and Difference
  6. Combinations of Functions: Product and Quotient
  7. Composition of Functions (the Chain Rule)
  8. Transformations of Functions
  9. Inverses of Functions
  10. Hyperbolic Functions
  11. Linear Approximation
  12. Mean Value Theorem

 

Chapter 4

Week of ... Monday Wednesday Thursday
10/10/11 Sec 4.1, 4.2
Extrema on an Interval
Rolle's Theorem, Mean Value Theorem		 Sec 4.3
Increasing/Decreasing
1st Derivative Test

Sec 4.4
Concavity
10/17/11

Sec 4.4 cont, Sec 4.6
2nd Derivative Test
Curve Sketching

 Sec 4.5
Limits at infinity

Q & A
10/24/11 Sec 4.7
Optimization		 Sec 4.7 cont.
Optimization

Sec 4.7 cont.
Optimization
10/31/11 Q & A Test #3  

Chapter 4 Homework Assignments

Sec 4.1 Page 209: 1, 2, 13, 15, 16, 17, 23, 27, 31, 33, 34, 75

Sec 4.2 Page 216: 11, 15, 17, 19, 33, 45, 47, 52, 63, 69-71

Sec 4.3 Page 226: 5, 6, 9, 10, 11, 15, 21, 27, 33, 35, 39, 41, 43, 46, 47, 69-72, 87, 93, 97, 99

Sec 4.4 Page 235: 15-27 odd, 29, 37, 43, 47, 63-70, 75, 79, 87

Sec 4.5 Page 245: 17-24

Sec 4.6 Page 255: 7, 9, 11, 15, 23, 25, 39, 43, 45,

Sec 4.7 Page 265: 2-6, 9-10, 13, 17, 19, 20, 22, 27-29, 42a, 43, 45, 47, 52, 60

Sec 4.8 Page 276: 25, 27, 31, 34, 35, 37, 41, 45, 47

 

Applets for Chapter 4 topics

Applications of Differentiation

  1. Curve Analysis: Basics
  2. Curve Analysis: Special Cases
  3. Curve Analysis: Global Extrema
  4. Optimization: Maximize Volume
  5. Extreme Value Theorem
  6. Related Rates
  7. L'Hopital's Rule
  8. Parametric Derivatives
  9. Polar Derivatives
  10. Motion on a Line
  11. Motion in the Plane

Chapter 5

Week of ... Monday Wednesday Thursday
10/31/11     Sec 5.1, 5.2
Antiderivative,
indefinite integrals and area
11/7/11 Sec 5.3
Riemann Sums and definite integrals		 Sec 5.3 cont
Riemann Sums and definite integrals		 SENIOR LAB DAY
11/14/11 Sec 5.4
Fundamental Theorem of Calculus		 Sec 5.5
Integration by Substitution		 Sec 5.5 cont
Integration by Substitution
11/21/11 Test #4 Thanksgiving

Holiday
11/28/11 Sec 5.6
Numerical Integration		 Sec 5.6 cont
Numerical Integration

Sec 5.6 cont
Numerical Integration
12/5/11 Sec 5.4
Differentials		 Sec 5.7
Integration of the natural log function

Sec 5.8
Integration of the inverse trig functions
12/12/11 Q & A for Final Exam SCIENCE EXAM
Tues, Dec 13, 2011		 MATH EXAM
Wed, Dec 14, 2011		 Sr Sem

Chapter 5 Homework Assignments

Sec 5.1 Page 291: 5, 7, 17, 21, 23, 25, 31, 33, 35, 43, 49, 50, 63, 67, 69, 70, 71, 74, 77, 79, 83, 85, 87, 93

Sec 5.2 Page 303: 15, 17, 19, 23-29 odd, 35, 39, 41, 47

Sec 5.3 Page 314: 1, 3-6, 9, 11, 17-19, 23, 25, 31, 45, 47,

Sec 5.4 Page 327: 5, 9, 13, 15, 27, 29, 31, 35, 37, 41, 57-63 odd, 73, 77, 93, 95

Sec 5.5 Page 340: 7-23 odd, 47-67 odd, 85, 95, 101, 103, 109, 125

Sec 5.6 Page 350: 1, 7, 17, 19, 23, 27-33 odd, 48, 54

Sec 5.7 Page 358: 1-7 odd, 13, 19, 25-31 odd, 35, 79, 85, 93

Sec 5.8 Page 366: 1-25 odd, 31, 35, 43, 45

Sec 5.9 Page 377: 7, 9, 10, 15-20, 29, 37, 39-45 odd, 57, 59, 73-79 odd

Sec 10.2 Page 717: 3-11 odd, 17, 51, 53

Sec 10.3 Page 725: 1, 3, 15, 16, 27, 31

Sec 10.4 Page 736: 1, 3, 5, 23-26, 27-41 odd, 81-86, 89, 91, 59, 60

Applets for Chapter 5 topics

Introduction to the Definite Integral

  1. Approximating Distance Traveled With a Table
  2. Approximating Distance Traveled With a Graph
  3. Riemann Sums and The Definite Integral
  4. Fundamental Theorem of Calculus
  5. Average Value
  6. Properties of Definite Integrals

Constructing Antiderivatives

  1. Antiderivatives from Slope and the Indefinite Integral
  2. Accumulation Functions
  3. Basic Antiderivatives
  4. Second Fundamental Theorem of Calculus
  5. Functions Defined Using Integrals
  6. Equations of Motion

Integration Techniques

  1. Substitution
  2. Midpoint and Trapezoid Riemann Sums