MA 136A - Calculus for Engineers I

• Understand the Mean Value Theorem
• Evaluate the limits of algebraic, trigonometric, exponential and logarithmic functions
• Identify removable and non-removable discontinuities
• Evaluate the derivative of algebraic, trigonometric, exponential and logarithmic functions
• Find the equation of a tangent line to a curve
• Find the position, velocity and acceleration of a moving object
• Use derivatives to find relative extrema and points of inflection on a curve
• Set up and solve optimization problems
• Set up and solve related rate problems

• Simplification of algebraic expressions containing complex fractions, exponents, and radicals
• Factoring
• Linear, fractional, and quadratic equations
• Cartesian coordinate system
• Systems of equations
• Trigonometric functions
• Trigonometric identities

• Algebra and trigonometry review (3 classes)
• Functions (3 classes)
• Limits and continuity (5 classes)
• Rates of change, tangent lines, and definition of derivative (2 classes)
• Derivatives of algebraic and trigonometric functions (6 classes)
• Derivatives of exponential and logarithmic and inverse trig functions (6 classes)
• First and second derivative tests for extrema, curve sketching (4 classes)
• Applied optimization problems (3 classes)
• Related rates problems (1 class)
• Mean Value Theorem (1 class)
• Review and exams (6 classes)