Dual Enrollment Program DE Course: Math 1530 Differential Calculus
Math 1530 Differential Calculus covers limits and derivatives of algebraic, exponential, logarithmic, and trigonometric functions, with applications.
This is an LSU Integrative Learning Core (ILC) course that awards general education credit. Math 1530 and Math 1540 together cover the material of LSU Math 1550. LSU credit will not be given for this course and Math 1431, Math 1550, or Math 1551.
Note: Math 1530 is designed for students who plan to major in a STEM field that requires calculus. This course fits better in the high school setting than a one-semester five-credit-hour calculus course because it is a three-credit-hour course that has content which can reasonably be covered in one semester. This course is taught in the fall followed by Math 1540 in the spring of the same school year. Students will need only one MyLab Math access code for this sequence.
Topics and Objectives
Chapter and section numbers refer to Calculus: Early Transcendentals, 3rd edition
2.1 The Idea of Limits
(11 exercises)
- Apply concepts related to limits
- Calculate average and instantaneous velocity
- Calculate slopes of secant and tangent lines
2.2 Definitions of Limits
(20 exercises)
- 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
(32 exercises)
- Apply techniques for computing limits
- Apply limit laws
- Evaluate limits
- Evaluate one-sided limits
- Use the Sandwich Theorem
2.4 Infinite Limits
(23 exercises)
- Apply properties of infinite limits
- Find infinite limits numerically or graphically
- Evaluate limits analytically
- Find vertical asymptotes
2.5 Limits at Infinity
(27 exercises)
- 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
(32 exercises)
- 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
(19 exercises)
- 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
(16 exercises)
- 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
(28 exercises)
- 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
(25 exercises)
- 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
(22 exercises)
- 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
(14 exercises)
- 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
(27 exercises)
- Apply properties of the chain rule
- Find derivatives using the chain rule
- Find equations of tangent lines
3.8 Implicit Differentiation
(21 exercises)
- 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
(31 exercises)
- 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
(22 exercises)
- 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
(20 exercises)
- 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
(28 exercises)
- 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
(16 exercises)
- 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
(16 exercises)
- 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
(14 exercises)
- 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] | 2025-04-23 |
| F25 Math 1530 DE Pacing Guide [docx] | 2025-04-23 |
Course Profile
| Name | Last Modified |
|---|---|
| Math 1530 Differential Calculus COURSE PROFILE 7-13-2022 [docx] | 2022-07-13 |
Class Notes
| Name | Last Modified |
|---|---|
| 2.1 The Idea of Limits [docx] | 2019-07-12 |
| 2.2 Definitions of Limits [docx] | 2019-07-12 |
| 2.3 Techniques for Computing Limits [docx] | 2019-07-12 |
| 2.4 Infinite Limits [docx] | 2019-07-12 |
| 2.5 Limits at Infinity [docx] | 2019-07-12 |
| 2.6 Continuity [docx] | 2019-07-12 |
| 3.1 Introducing the Derivative [docx] | 2019-07-12 |
| 3.2 Working with Derivatives [docx] | 2019-07-12 |
| 3.3 Rules of Differentiation [docx] | 2019-07-12 |
| 3.4 The Product and Quotient Rules [docx] | 2019-07-12 |
| 3.5 Derivatives of Trigonometric Functions [docx] | 2019-07-12 |
| 3.6 Derivatives as Rates of Change [docx] | 2019-07-12 |
| 3.7 The Chain Rule [docx] | 2019-07-12 |
| 3.8 Implicit Differentiation [docx] | 2019-07-12 |
| 3.9 Derivatives of Logarithmic and Exponential Functions [docx] | 2019-07-12 |
| 3.10 Derivatives of Inverse Trigonometric Functions [docx] | 2019-07-12 |
| 3.11 Related Rates [docx] | 2019-07-12 |
| 4.1 Maxima and Minima [docx] | 2019-07-12 |
| 4.3 What Derivatives Tell Us [docx] | 2019-07-12 |
| 4.4 Graphing Functions [docx] | 2019-07-12 |