Science:Math Exam Resources/Courses/MATH100/Syllabus

The Tangent and Velocity Problems
The Limit of a Function
Calculating Limits Using the Limit Laws
Continuity
Limits at Infinity; Horizontal Asymptotes
Derivatives and Rates of Change
The Derivative as a Function
Derivatives of Polynomials and Exponential Functions
The Product and Quotient Rules
Derivatives of Trigonometric Functions
The Chain Rule
Inverse Functions and Logarithms
Implicit Differentiation
Derivatives of Logarithmic Functions
Rates of Change in the Natural and Social Sciences
Exponential Growth and Decay
Related Rates
Linear Approximations and Differentials
Taylor Polynomials
Taylor’s Formula with Remainder
Maximum and Minimum Values
The Mean Value Theorem
How Derivatives Affect the Shape of a Graph (First and Second Derivative Tests)
Summary of Curve Sketching
Optimization Problems
Newton’s Method
Antiderivatives