Calculus

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Course Outline: 

Chapter P: Prepartions of Calculus

Graphs and Models
Linear Models and Rates of Change
Functions and Their Graphs
Fitting Models and Data
Transformations
Equations and Inequalities
Relations, Functions and Inverses

Chapter 1 Limits and Their Properties

Estimate a limit using numerical and graphical techniques
Learn different ways a limit can fail to exist
Use the formal definition of a limit
Evaluate a limit using properties of limits
Evaluate a limit using cancellation and rationalization
Evaluate a limit using the squeeze theorem
Determine continuity at a point and on an open interval
Determine one-sided limits and continuity on a closed interval
Understand and use the Intermediate Value Theorem
Determine infinite limits 
Find and sketch the vertical asymptotes of a function
Find the slope of a tangent line to a curve at a point

Chapter 2 Differentiation

Use the limit definition to find the derivative of a function
Understand the relationship between differentiability and continuity
Find the derivative of a function using the constant, power, constant multiple, and sum and difference rules
Find the derivative of the trigonometric functions
Use derivatives to find rates of change
Find the derivative using the product and quotient rule
Find the higher order derivative of a function
Find the derivative of a composite function using the chain rule
Use implicit differentiation
Find related rates and use to solve real-life problems

Chapter 3 Applications of Differentiation

Understand relative and absolute extrema
Find extrema on a closed interval
Understand and use Rolle’s Theorem and the Mean Value Theorem
Recognize the situations where the derivative is needed
Use the derivative to determine intervals of increasing, decreasing, concave up, and concave down.
Use the first and second derivative test to find relative extrema
Find points of inflection
Determine horizontal asymptotes if any
Analyze and sketch the graph of a function
Solve applied minimum and maximum problems
Write the general solution to a differential equation

Chapter 4 Integration

Use indefinite integral notation for antiderivatives
Use basic integration rules to find antiderivatives
Find a particular solution of a differential equation. write the general solution of a differential equation.
Use sigma notation to write and evaluate a sum.
Find the area of a plane region using limits.
Evaluate a definite integral using limits of a Riemann sum.
Evaluate a definite integral using the Fundamental theorem of Calculus.
Find the average value of a function over a closed interval.
Use the Substitution method to evaluate a definite integral.

Chapter 5 Logarithmic, Exponential, and Other Transcendental Funtions

Find the derivative of the exponential and logarithmic functions
Find the integral of the exponential and logarithmic functions
Find the derivative of the Bases Other Than e and Applications
Find the derivative of the Inverse Trigonometry Functions
Find the integral of the Inverse Trigonometry Functions