LSC-CyFair Math Department
Functions, limits, continuity, differentiation and integration of algebraic and trigonometric functions, applications of differentiation and an introduction to applications of the definite integral.
Course Learning Outcomes
The student will:
• Develop solutions for tangent and area problems using the concepts of limits, derivatives, and integrals.
• Draw graphs of algebraic and transcendental functions considering limits, continuity, and differentiability at a point.
• Determine whether a function is continuous and/or differentiable at a point using limits.
• Use differentiation rules to differentiate algebraic and transcendental functions.
• Identify appropriate calculus concepts and techniques to provide mathematical models of real-world situations and determine solutions to applied problems.
• Evaluate definite integrals using the Fundamental Theorem of Calculus.
• Articulate the relationship between derivatives and integrals using the Fundamental Theorem of Calculus.
• Use implicit differentiation to solve related rates problems.
Contact Hour Information
Credit Hours: 4
Lecture Hours: 3
Lab Hours: 2
External Hours: 0
Total Contact Hours: 80
MATH 2412 OR placement by testing;
ENGL 0305 or ENGL 0365 OR higher level course (ENGL 1301), OR placement by testing
Chapter 2. Limits and Continuity
2.1 Rates of Change and Tangents to Curves
2.2 Limit of a Function and Limit Laws
2.3 The Precise Definition of a Limit
2.4 One-Sided Limits and Limits at Infinity
2.5 Infinite Limits and Vertical Asymptotes
2.7 Tangents and Derivatives at a Point
Chapter 3. Differentiation
3.1 The Derivative as a Function
3.2 Differentiation Rules
3.3 The Derivative as a Rate of Change
3.4 Derivatives of Trigonometric Functions
3.5 The Chain Rule
3.6 Implicit Differentiation
3.7 Related Rates
3.8 Linearization and Differentials (optional)
Chapter 4. Applications of Derivatives
4.1 Extreme Values of Functions
4.2 The Mean Value Theorem
4.3 Monotonic Functions and the First Derivative Test
4.4 Concavity and Curve Sketching
4.5 Applied Optimization
4.6 Newton’s Method (optional)
Chapter 5. Integration
5.1 Area and Estimating with Finite Sums
5.2 Sigma Notation and Limits of Finite Sums
5.3 The Definite Integral
5.4 The Fundamental Theorem of Calculus
5.5 Indefinite Integrals and the Substitution Rule
5.6 Substitution and Area Between Curves
Chapter 6. Applications of Definite Integrals
6.1 Volumes by Slicing and Rotation About an Axis
6.2 Volumes by Cylindrical Shells
6.3 Lengths of Plane Curves
6.4 Areas of Surfaces of Revolution