Dual Enrollment Program: DE Course Math 1530
Math 1530 Differential Calculus covers limits and derivatives of algebraic, exponential, logarithmic, and trigonometric functions, with applications.
Topics and Objectives
Section numbers refer to Calculus: Early Transcendentals, 3e (Briggs, Cochran, Gillett, Schultz).
2.1 The Idea of Limits
- Apply concepts related to limits
- Calculate average and instantaneous velocity
- Calculate slopes of secant and tangent lines
2.2 Definitions of Limits
- Apply limit definitions
- Find limits from a graph
- Estimate limits from a table
- Study limits for particular well-known functions
2.3 Techniques for Computing Limits
- Apply techniques for computing limits
- Apply limit laws
- Evaluate limits
- Evaluate one-sided limits
- Use the Sandwich Theorem
2.4 Infinite Limits
- Apply properties of infinite limits
- Find infinite limits numerically or graphically
- Evaluate limits analytically
- Find vertical asymptotes
2.5 Limits at Infinity
- Apply concepts relating to end behavior and horizontal asymptotes
- Evaluate limits at infinity
- Find horizontal asymptotes of rational functions
- Determine end behavior and sketch graphs
- Find horizontal and vertical asymptotes
- Use limits to find steady states in applications
- Find limits of sequences
2.6 Continuity
- Apply the concept of continuity
- Find points of discontinuity or intervals of continuity
- Determine whether a function is continuous at a point using the continuity checklist
- Evaluate limits using principles of continuity
- Use the Intermediate Value Theorem
- Classify discontinuities
3.1 Introducing the Derivative
- Review the concept of the derivative
- Use limit definitions to find equations of tangent lines
- Understand differentiability and relate it to continuity
- Understand derivatives graphically
- Solve applications involving basic derivatives
3.2 Working with Derivatives
- Apply concepts related to working with derivatives
- Work with the graph of the derivative of a function
- Find derivatives of functions using limits
- Determine continuity and differentiability and evaluate derivatives
- Understand differentiability and relate it to continuity
3.3 Rules of Differentiation
- Use graphs and tables to find derivatives
- Find derivatives using rules of differentiation
- Simplify products and quotients and find their derivatives
- Use derivatives to find slope locations and equations of tangent lines
- Find higher-order derivatives of functions
- Find limits related to derivatives
3.4 The Product and Quotient Rules
- Find derivatives of products and quotients of algebraic expressions
- Find derivatives using two different methods
- Find derivatives using the extended power rule
- Find higher order derivatives of products and quotients
- Find derivatives of products and quotients using given values or graphs
- Find equations of tangent lines
3.5 Derivatives of Trigonometric Functions
- Find derivatives of basic trigonometric functions
- Find limits involving trigonometric functions
- Find derivatives of products, quotients, and powers of functions with trigonometric expressions
- Find higher order derivatives of functions involving trigonometric expressions
- Verify statements involving trigonometric expressions
- Find equations of tangent lines
3.6 Derivatives as Rates of Change
- Apply concepts related to derivatives as rates of change
- Relate position, velocity, and acceleration to derivatives
- Solve other applications involving derivatives as rates of change
3.7 The Chain Rule
- Apply properties of the chain rule
- Find derivatives using the chain rule
- Find equations of tangent lines
3.8 Implicit Differentiation
- Apply the concept of implicit differentiation
- Find derivatives using implicit differentiation
- Find equations of tangent lines using implicit differentiation
- Find derivatives of functions with rational exponents
- Find tangent and normal lines
- Solve applications using implicit differentiation
3.9 Derivatives of Logarithmic and Exponential Functions
- Find derivatives involving logarithms and exponential
- Find derivatives using logarithmic differentiation
- Evaluate limits of logarithmic and exponential functions using the definition of the derivative
3.10 Derivatives of Inverse Trig Functions
- Apply concepts relating to the derivatives of inverse trigonometric functions
- Find derivatives of functions involving inverse trigonometric functions
- Find equations of tangent lines
- Find derivatives of general inverse functions
- Solve applications involving the rate of change of an angle with respect to a side
3.11 Related Rates
- Solve related rates problems involving geometry
- Solve related rates applications for the rate of change of distance, area, or volume
- Solve related rates applications for the rate of change of an angle
4.1 Maxima and Minima
- Apply concepts related to maxima and minima
- Use graphs to illustrate or identify extreme points
- Find critical points and extreme points
- Solve applications involving extreme points
4.3a What Derivatives Tell Us
- Find intervals on which a function is increasing and decreasing
- Use the first derivative test to find local and absolute extrema
4.3b What Derivatives Tell Us
- Sketch functions from properties
- Determine the concavity on intervals and find inflection points
- Use the second derivative test to find local extrema
- Compare f, f', and f''
4.4 Graphing Functions
- Sketch functions using analytic methods
- Graph functions, and find any local extrema and inflection points
- Sketch the general graph of functions given the equation of the derivatives
Syllabus & Pacing Guide
| Name | Last Modified |
|---|---|
| F25 Math 1530 DE Syllabus.docx [docx] | 2025-04-23 |
| F25 Math 1530 DE Pacing Guide.docx [docx] | 2025-04-23 |
Course Profile
| Name | Last Modified |
|---|---|
| Math 1530 Differential Calculus COURSE PROFILE 7-13-2022 [docx] | 2022-07-13 |