Prerequisite: Completion of MATH 135 , Completion of MATH 140 or Completion of MATH 130 and
Advisory: Eligibility for College Level Reading (CLR) , Eligibility for MATH 150
This course is for the student planning upper-division work in math, physics, engineering, or business. It involves differentiation and integration of algebraic, trigonometric, exponential, and logarithmic functions. Applications include extrema, graphing, related rates, and area. (CSU, UC, AVC)
- Limits and Their Properties
- Finding limits graphically and numerically
- Evaluating limits analytically
- Continuity and one-sided limits
- Infinite limits
- Differentiation
- The derivative and the tangent line problem
- Basic differentiation rules and rates of change
- The product and quotient rules
- Higher-order derivatives
- The chain rule
- Implicit differentiation
- Related rates
- Applications of Differentiation
- Extrema on an interval
- Rolle's Theorem and the Mean Value Theorem
- Increasing and decreasing functions and the First Derivative Test
- Concavity and the Second Derivative Test
- Limits at infinity
- Curve sketching
- Optimization problems
- Integration
- Antiderivatives and indefinite integration
- Area
- Riemann sums and definite integrals
- The Fundamental Theorem of Calculus
- Integration by substitution
- Numerical integration
- Logarithmic, Exponential and Other Transcendental Functions
- Differentiation and integration of logarithmic functions
- Differentiation and integration of exponential functions
- Differentiation and integration of trigonometric functions and their inverses
- Differentiation and integration of hyperbolic functions and their inverses
Reading and understanding the contents of the textbook including formulas, definitions, theorems, algorithms, and examples are required on a daily basis.
Students are sometimes asked to give short answers and explanations related to the computational work and the meaning and applicability of theorems.
Computational assignments are made for most class meetings. Assignments usually consist of textbook exercises from one or two sections.
Students may be encouraged but not required to use technological resources, software, and graphing calculators to reinforce concepts and skills presented in lecture.