The following list of objectives is designed to give you some guidance at what topics are important from the various sections we will cover from the book.  These objectives are some of the key concepts that will be discussed for each section.  When you take exams in this course you must show me your work to earn full credit for a problem.  Correct answers with no work shown will be penalized. Partial credit will be given on problems therefore showing your work is vital to your grade and it also allows me to better determine where your weakness may be if you need assistance with any of the material.

MATH222 CHAPTER 7 OBJECTIVES

SECTION 7.1  Examples of Functions of Several Variables
1)  Evaluate a function of several variables at a specific point.
2)  Be able to draw level curves.

SECTION 7.2  Partial Derivatives
1) Find  first partial derivatives of multivariable functions
2) Find first partial derivatives at a specific point
3) Find the second partial derivatives of multivariable functions.

SECTION 7.3  Maxima and Minima of Functions of Several Variables
1) Use the second derivative test for a function of two variables to find any local extrema of the bivariate function.
Note: This means you will set the first partial derivatives to equal zero.  Therefore, you will need to be comfortable with solving systems of equations which may not involve linear functions.

SECTION 7.4 Lagrange Multipliers and Constrained Optimization
1) Use the Lagrangian to determine the minimum or maximum of an optimization problem with a single inequality constraint

TOTAL DIFFERENTIALS HANDOUT
1) Find the approximate values of functions by using total differentials.

SECTION 7.5 The Method of Least Squares
1) Given a set of observed data points determine the straight line that “best” fits the observations using the algebraic formulas for slope and intercept.
2) Given a set of observed data points determine using partial derivatives the straight line that has the minimum sum of squared error (called the method of least squares)

SECTION 7.7 Double Integrals
1) Evaluate iterated integrals
 

MATH222 CHAPTER 8 OBJECTIVES

SECTION 8.1 Radian Measure of Angles
1) Convert between radians and degrees
2) Construct angles with a specified radian measure

SECTION 8.2 The Sine and the Cosine
1) Use sint = y/r or opposite/hypotenuse to give the value of sint
2) Use cost = x/r or adjacent /hypotenuse to give the value of cost
3) Use properties of sine and cosine functions

SECTION 8.3 Differentiation and Integration of sint and cost
1) Find the derivatives of sin(g(t)) and cos(g(t))
2) Use any of the derivative rules to take derivatives of expressions involving sine or cosine functions
3) Integrate sin(g(t)) or cos(g(t))

SECTION 8.4 The Tangent and Other Trigonometric Functions
1) Use tant = sint/cost or y/x to give values for tant
2) Work with Pythagorean identities
3) Find derivatives of tan(g(t))
4) Differentiate functions that involve the tangent
 

MATH222 CHAPTER 9 OBJECTIVES

SECTION 9.1 Integration by Substitution
1) Be able to integrate using u substitution.  If u substitution is appropriate the integration becomes one of our three basic types, e^x, 1/x, or x^r.  This means try using u as the exponent if e is involved, the denominator if a fraction is involved , or as what is being raised to a power if powers are involved (higher power).  We now will include the trigonometric functions for this section which is revisited from Calculus I.

SECTION 9.2 Integration by Parts
1) When u substitution is not appropriate, you will need to know how to integrate by parts.  If e^x is involved it is g prime, if lnx is involved it is f(x) otherwise choose f(x) so that it has a “nicer” derivative. We now will include the trigonometric functions for this section, which is revisited from Calculus I.

SECTION 9.3 Evaluation of Definite Integrals
1) Evaluate definite integrals involving u substitution or parts.

SECTION 9.4 Approximation of Definite Integrals
1) Use the midpoint rule to approximate the value of a definite integral
2) Use the trapezoidal rule to approximate the value of a definite integral
3) Use Simpson’s rule to approximate the value of a definite integral

PARTIAL FRACTIONS HANDOUT
1) Use partial fractions technique to handle integrals of the form p(x)/q(x) where both p(x) and q(x) are polynomials

SECTION 9.5 Some Applications of the Integral
1) Find the present value of an income stream
2) Find the total population in a ring around a city center

SECTION 9.6 Improper Integrals
1) Evaluate improper integrals using limits.
 

MATH222 CHAPTER 10 OBJECTIVES

SECTION 10.1 Solutions of Differential Equations
1) Show a particular function is a solution to a given differential equation
2) Find the solution to a simple differential equation (solve an initial value problem)

SECTION 10.2 Separation of Variables
1) Solve differential equations in which the variables can be separated
2) Solve variables separable differential equations with given initial conditions

SECTION 10.3 Numerical Solution of Differential Equations
1) Use Euler’s Method to approximate the solution to a differential equation on a specified interval
 

MATH222 CHAPTER 12 OBJECTIVES

SECTION 12.1 Discrete Random Variables
1) Determine the mean, variance, and standard deviation for a given discrete probability distribution
2) Find expected values or variances for probability distributions from a word problem

SECTION 12.2 Continuous Random Variables
1) Verify a function is a probability density function
2) Determine the value k that makes a given function a probability density function
3) Find probabilities on specified intervals given the density functions

SECTION 12.3 Expected Value and Variance
1) Find the expected value and variance for continuous probability distributions

SECTION 12.4 Exponential and Normal Random Variables
1) Work with Exponential density functions
2) Work with Normal density functions
3) Be able to find normal probabilities using z-scores and the normal probability tables

SECTION 12.5 Poisson and Geometric Random Variables
1) Compute probabilities for Poisson distributions (usually involve a counting process)
2) Compute probabilities for Geometric distributions (experiment continues until the first time a particular outcome is observed)
 

MATH222 CHAPTER 11 OBJECTIVES

SECTION 11.1 Taylor Polynomials
1) Find the nth Taylor polynomial of f(x) at x =0
2) Find the nth Taylor polynomial of f(x) at x =a

SECTION 11.2 The Newton Raphson Algorithm
1) Use the Newton Raphson algorithm to approximate the zeros of a function

SECTION 11.3 Infinite Series
1) Determine whether a geometric series converges or diverges
2) Calculate the sums of geometric series
3) Determine the sums of infinite series

RATIO TEST HANDOUT
1) Use the ratio test to determine if an infinite series is convergent or divergent

SECTION 11.4 Series with Positive Terms
1) Apply the integral test to determine if a series is convergent or divergent
2) Use the comparison test to determine if a series is convergent or divergent

SECTION 11.5 Taylor Series
1)  Find the Taylor series expansion of a function at x = 0