Mth 272, Applied Calculus I

Assignments Table, Full Version

If you have not yet done so, you need to read the information in the Initial Information document and work through the Orientation and Startup to which that document refers you.

It is necessary to have done so in order to understand this page and to use it properly.

How to Complete Assignments

Table of Assignments, Topics and Specific Objectives

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Complete Orientation according to Initial Instructions document
 

 

Strongly recommended but not required:  Complete the Recommended Review of Calculus I Topics

 

 

 

Table of Assignments and Objectives

 

 
Module 1, Review of Exponential and Logarithmic functions and their Derivatives

Test 1 should be taken within a week of completing Module 1.
Asst Read, take notes, etc. Problems DVD   class notes other query  
01 Text Sections 4.1-4.3 Chapter 4 problems for Sections 4.1-4.3         query_01  
Objectives:
  • Use the properties of exponents to evaluate and simplify exponential expressions.
  • Sketch the graphs of exponential functions.
  • Evaluate and graph functions involving the natural exponential function.
  • Solve compound interest problems.
  • Solve present value problems.
  • Find derivatives of natural exponential functions.
  • Use calculus to analyze the graphs of functions that involve the natural exponential functions.
  • Explore the normal probability density function.

 
02 Text Section 4.4 Chapter 4 problems for Section 4.4         query_02  
Objectives:
  • Sketch the graphs of natural logarithmic functions.
  • Use properties of logarithms to simplify, expand, and condense logarithmic expressions.
  • Use inverse properties of exponential and logarithmic functions to solve exponential and logarithmic equations.
03 Text Section 4.5 Chapter 4 problems for Section 4.5         query_03  
Objectives:
  • Find derivatives of natural logarithmic functions.
  • Use calculus to analyze the graphs of functions that involve the natural logarithmic function.
  • Use the definition of logarithms and the change-of-base formula to evaluate logarithmic expressions involving other bases.
  • Find derivatives of exponential and logarithmic functions involving other bases.
04 Text Section 4.6 Chapter 4 problems for Section 4.6         query_04  
Objectives:
  • Use exponential growth and decay to model real-life situations.
Module 2, Integration and its Applications

Test 2 should be taken within a week of completing Module 2.
05 Text Section 5.1 Chapter 5 problems  for Section 5.1, Part 1

With Assignments 5 and 6, View Class Notes #01, which gives an overview of integration and assumes you have viewed the Introduction to Integration clips (ignore section numbers, which are for Chapter 6 of a different text)

   Class Notes

 # 01

 		   query_05  
Objectives:
  • Understand the definition of antiderivative.
  • Use indefinite integral notation for antiderivatives.
  • Use basic integration rules to find antiderivatives.
  • Use initial conditions to find particular solutions of indefinite integrals.
  • Use antiderivatives to solve real-life problems.
06 Text Section 5.2 Chapter 5 problems for Section 5.1, Part II         query_06  
Objectives:
  • Use the General Power Rule to find indefinite integrals.
  • Use substitution to find indefinite integrals.
  • Use the General Power Rule to solve real-life problems.
07 Text Section 5.3 Chapter 5 problems for Section 5.2, Part II and 5.3     Class Notes

 # 02

 		   query_07  
Objectives:
  • Use the Exponential Rule to find indefinite integrals.
  • Use the Log Rule to find indefinite integrals.
08 Text Section 5.4 Chapter 5 problems for Section 5.4

View Class Notes #03 on Integrals and Differential Equations

   Class Notes

 #03

   query_08  
Objectives:
  • Evaluate definite integrals.
  • Evaluate definite integrals using the Fundamental Theorem of Calculus.
  • Use definite integrals to solve marginal analysis problems.
  • Find the averfage values of functions over closed intervals.
  • Use properties of even and odd functions to help evaluate definite integrals.
  • Fiud the amounts of annuities.
09 Text Section 5.5 Chapter 5 problems for Section 5.5, Part I

View Class Notes #05, concentrating on Differential Equations for Free Fall; 2d Fundamental Theorem is optional.

   Class Notes

 # 05

   query_09  
Objectives:
  • Find the areas of regions bounded by two graphs.
  • Find consumer and producer surpluses.
  • Use the areas of regions bounded by two graphs to solve real-life problems.
10 Text Section 5.5 Chapter 5 problems for Section 5.5, Part II         query_10  
 
11 Text Section 5.6 Chapter 5 problems for Section 5.6, Part I         query_11  
Objectives:
  • Use the Midpoint Rule to approximate definite integrals.
  • Use a symbolic integration utility to approximate definite integrals.
12 Text Section 5.6 Chapter 5 problems for Section 5.6, Part II         query_12  
 
13 Text Section

Section 5.7, Problems 2, 3, 4, 12, 13, 16, 17, 18, 22, 30, 31

         query_13  
Objectives:
  • Use the disk method to find volumes of solids of revolution.
  • Use the Washer Method to find volumes of solids of revolution with holes.
  • Use solids of revolution to solve real-life problems.
Module 3, Techniques of Integration

Test 3 should be taken within a week of completing Module 3.
14 Text Section

Section 6.1, Problems 2, 5, 8, 11, 13, 16, 25, 26, 31, 32, 37, 38, 45, 46, 50, 51, 54, 55, 56, 59, 64

View Class Notes #04.  Concentrate on Integration by Substitution.  The 2d Fundamental Theorem is optional.

   Class Notes

 # 04

   query_14  
Objectives:
  • Use the basic integration formulas to find indefinite integrals.
  • Use substitution to find indefinite integrals.
  • Use substitution to evaluate definite integrals.
  • Use integration to solve real-life problems.
15 Text Section

Section 6.2, Problems 1, 2, 3, 5, 9, 10, 17, 18, 29, 30, 32, 34

View Class Notes #07 and #08 on Integration by Parts and Substitution; the discussion of the differential equation at the beginning is optional.   Examples involving trigonometric functions are optional but informative.

   Class Notes

 # 07, 08

   query_15  
Objectives:
  • Use integration by parts to find indefinite and definite integrals.
  • Find the present value of future income.
16 Text Section Section 6.2, Problems 48, 50*, 51*, 54, 57, 60, 62, 65, 68

View Class Notes #09 on Integration by Parts.   Examples involving trigonometric functions are optional but informative.

   Class Notes

 # 09

   query_16  
 
17 Text Section Section 6.3, Problems 5, 6, 17, 18, 27, 28

View Class Notes #10 on Integration Techniques.   Examples involving trigonometric functions are optional but informative.

   Class Notes

 # 10

   query_17  
Objectives:
  • Use partial fractions to find indefinite integrals.
  • Use logistic growth functions to model real-life situations.
18 Text Section Section 6.3, Problems 37, 38, 53, 54, 55, 56, 57, 58

View Class Notes #11 on Integration by Tables.   Examples involving trigonometric functions are optional but informative.

   Class Notes

 # 11

   query_18  
 
19 Text Section Section 6.4, Problems 1, 3, 5, 8, 13, 16, 21, 32, 46, 47, 49, 53, 56, 64

View Class Notes #12 on Integration by Approximation.

 		   Class Notes

 # 12

   query_19  
Objectives:
  • Use integration tables to find indefinite integrals.
  • Use reduction formulas to find indefinite integrals.
  • Use completing the square to find indefinite integrals.
20 Text Section Section 6.5, Problems 2, 3, 9,  10 , 15, 16,  19 , 29, 30, 33, 34, 37, 46, 49         query_20  
Objectives:
  • Use the Trapezoidal Rule to approximate definite integrals.
  • Use Simpson's Rule to approximate definite integrals.
  • Analyze the sizes of the errors when approximating definits integrals with the Trapezoidal Rule and Simpsons's Rule.
21 Text Section Section 6.6, Problems 1, 2, 6, 9, 14 , 25, 28,  38 , 39         query_21  
Objectives:
  • Recognize improper integrals.
  • Evaluate improper integrals with infinite limts of integrations.
  • Evaluate improper integrals with infinite integrands.
  • Use improper integrals to solve real-life problems.
 
Module 4, Functions of Several Variables

Test 4 should be taken prior to the last day of final exams.
22 Text Section Section 7.1, Problems 1-4, 6, 7, 11, 14, 15, 18,  24 , 26, 7, 31, 32, 35, 39, 42     Class Notes Disk 7a

Demonstration:  3-dimensional

Distance Formula in 3 dimensions

Equation of a Sphere

Sphere in Space

Traces in Coordinate Planes

Traces in Planes Parallel to Coordinate Planes

   query_22  
Objectives:
  • Plot points in space.
  • Find distances between points in space and find midpoints of line segments in space.
  • Write the standard forms of the equations of spheres and find the centers and darii of spheres.
  • Sketch the coordinate plane traces of surfaces.
23 Text Section Section 7.2, Problems 5,  6 , 10, 11, 17, 23, 27, 31-34     Class Notes Disk 7a

Equation of a Plane

Equation of a Plane part 2

Equations of Various Special Planes

Conic Sections:  Review

Quadric Surfaces

A Paraboloid

   query_23  
Objectives:
  • Sketch planes in space.
  • Draw planes in space with different numbers of intercepts.
  • Classify quadric surfaces in space.
24 Text Section Section 7.2, Problems 36, 37, 43,   48 , 52         query_24  
 
26 Text Section Section 7.3, Problems 2,  3 , 6, 9, 13,  14 , 15,  18 , 29-32     Class Notes Disk 7a

Representing a Function of 2 variables by a Table

Level Curves

   query_26  
Objectives:
  • Evaluate functions of several variables.
  • Find the domains and ranges of functions of several variables.
  • Read contour maps and sketch level curves of functions of two variables.
  • Use functions of several variables to answer questions about real-life situations.
27 Text Section Section 7.3, Problems 34,  35 , 38, 39, 42,  46 , 49         query_27  
 
28 Text Section Section 7.4, Problems 2, 3, 8, 11,    14 , 16, 17, 23,  32, 36 , 37, 40     Class Notes Disk 7a

Function of 2 variables defined by an Integral with Variables as Limits

Difference Quotient

Domain of a Function of 2 variables

Another Function, another domain

Happiness-at-a-meeting Model and Partial Derivatives

Partial Derivatives of the Happiness Function

Partial Derivative of a Modified Happiness Function

Geometric Interpretation of Partial Derivatives

Slope of a Surface at a Point

Demonstration of Partial Derivatives on a Christmas Tree Ornament

A Demand Function of Two Variables

Marginal Costs

   query_28  
Objectives:
  • Find the first partial derivatives of functions of two variables.
  • Find the slopes of surfaces in the x- and y-directions and use partial derivatives to answer questions about real-life situations.
  • Find the partial derivatives of functions of several variables.
  • Find higher-order partial derivatives.
29 Text Section Section 7.4, Problems 41, 46, 48, 49,  50, 56 , 60, 65, 68, 71, 74         query_29  
 
30 Text Section Section 7.5, Problems 1, 4, 7, 10, 13, 17, 20, 27, 28     Class Notes Disk 7a

Contour-line Example of Maxima and Minima

Critical Points of a Function of Two Variables

Maximum or Minimum of a Paraboloid

Trickiness of Saddle Points

Test for Maxima and Minima

Applying the Test for Maxima and Minima

   query_30  
Objectives:
  • Understand the relative extrema of functions of two variables.
  • Use the First-Partials test to find the relative extrema of functions of two variables.
  • Use the Second-Partials Test to find the relative extrema of functions of two variables.
  • Use relative extrema to answer questions about real-life situations.
31 Text Section Section 7.7, Problems 1, 4, 6, 9, 13, 16, 19, 22, 27, 30 , 33, 34     Class Notes Disk 7b

Fitting a Straight Line to Data

Finding Squared Error

Minimizing Squared Error

Using the Least-Squares Line

Generalizing the Process

   query_31  
Objectives:
  • Find the sum of the squared errors for mathematical models.
  • Find the least squares regression lines for data.
  • Find the least squares regression quadratics for data.
32 Text Section Section 7.8, Problems 3,  6 , 9, 10, 11, 14, 19  22 , 31, 32, 37, 40, 44     Class Notes Disk 7b

Evaluating a Double Integral

Describing a Region in the Plane

Area of a Region in the Plane

Reversing the Order of Integration

Volume of a Solid, I

Volume of a Solid, II

Double Integral of Population Density

Average Value of a Function of Two Variables

Calculating Average Values

   query_32  
Objectives:
  • Evaluate double integrals.
  • Use double integrals to find the areas of regions.
33

Prepare for and complete Chapter 7 Test and Cumulative Final Exam in Learning Lab or Approved Facility