- Course type: Self-paced
- Available Lessons: 105
- Average Lesson Length: 8 min
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Watch a preview:chapter 1 / lesson 1What is a Function: Basics and Key Terms
Course SummaryThis Calculus Syllabus Resource & Lesson Plans course is a fully developed resource to help you organize and teach calculus. You can easily adapt the video lessons, transcripts, and quizzes to take full advantage of the comprehensive and engaging material we offer. Make planning your course easier by using our syllabus as a guide.
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Course Practice TestCheck your knowledge of this course with a 50-question practice test.
- Comprehensive test covering all topics
- Detailed video explanations for wrong answers
How It Works
You can use this calculus course as a template for designing and implementing your course. Here are the key components of the course and how you can use them:
- Chapters - Each chapter covers a unit of calculus, from graphing and functions to integrals and differential equations. Use these chapters as mile markers as you map out your course. We recommend planning to spend a week on each chapter, but you can always allocate the chapters according to the length of your specific calculus course.
- Lessons - Within each chapter are video lessons that further break down topics into bite-sized chunks. These lessons cover single topics like 1-sided limits or the trapezoid rule. Each one is often appropriate for a single class.
- Key Terms - Within each lesson are key terms. These are emphasized on screen and in the transcript. As you develop your syllabus, these key terms help you focus on the most important learning objectives. For example, the lesson on function discontinuities includes key terms like point discontinuities, jump discontinuities, and asymptotic discontinuity.
As you work on your calculus lesson plans, save time by incorporating video lessons from this resource. Here's how:
- Introduce Topics - Your students will be in the right mindset for understanding topics like derivatives if you begin class with a short video. It can be a jumping-off point for a lecture, group activity, or class discussion.
- Break Up Lectures - The video format, which often includes animation, helps students visualize topics like the mean value theorem and L'Hopital's rule.
- Assign For Homework - Each lesson in the course, from function basics to rate calculations, can be assigned to your students as homework.
Each video lesson includes a complete transcript. You can utilize these transcripts in several ways:
- Lecture Notes - Do you need a guide as you plan a lecture, such as one on continuity or limits? The transcripts cover each topic in depth, with key terms highlighted for quick reference.
- Student Reading - Perhaps you'd like your students to learn about the arc length of a function, but you don't have class time available. Assign the transcript as extra reading.
- Study Tools - When it's time for a unit exam on integrals, you can point your students to the transcripts on Riemann sums, the fundamental theorem of calculus, and related topics to help them study.
Each video lesson has a corresponding quiz. Here's how to use the quizzes:
- Homework - Assign a quiz to your students as homework. You'll receive an email with the results, which enables you to verify they've completed the assignment and that they've understood the material. Questions cover everything from methods for interpreting function graphs to techniques for calculating their derivatives and integrals.
- Tests - You can meld the material in the quizzes into your own student assessments, saving you valuable time. Need a few questions on the rate of change? There are plenty!
- Discussions - Jump-start a discussion with questions like: What are some of the applications of the intermediate value theorem?
Below is a sketch of the calculus syllabus modeled on a 13-week course. This sample can be adapted based on your course schedule. Navigate the chapters and lessons for more detail.
|Week||Unit||Sample of Topics Covered|
|Week 1||Graphing and Functions||Functions of functions, graphs of inverse functions and quadratic functions, the natural log, point-slope formula, implicit functions, asymptotes|
|Week 2||Continuity||Regions of continuity, types of discontinuities, applications of the intermediate value theorem|
|Week 3||Geometry and Trigonometry||Volumes of 2D and 3D shapes, the Pythagorean theorem, graphs of sine and cosine|
|Week 4||Using Scientific Calculators||Radians and degrees on scientific calculators, trig functions and exponentials, graphing|
|Week 5||Limits||Limit notation, 1-sided limits, limit properties, the squeeze theorem, limits for asymptotes|
|Week 6||Rate of Change||The relationship between slope and the rate of change, the mean value theorem, Rolle's theorem, graphical representations of derivatives|
|Week 7||Calculating Derivatives and Derivative Rules||Derivatives of trigonometric functions and polynomial equations, the chain rule, the product and quotient rules|
|Week 8||Graphing Derivatives and L'Hopital's Rule||Maximum and minimum values of graphs, concavity and inflection points, applications of L'Hopital's Rule|
|Week 9||Applications of Derivatives||Linearization of functions, Newton's method, differentiation, simple and complex system optimization|
|Week 10||Area Under the Curve and Integrals||Riemann sums, the trapezoid rule, indefinite and definite integrals, the average value theorem, the fundamental theorem of calculus|
|Week 11||Integration and Integration Techniques||Integrals of trigonometric and exponential functions, integration by parts, trigonometric substitution, improper integrals|
|Week 12||Integration Applications||Integration and dynamic motion, methods for finding the area between functions and volumes of revolution|
|Week 13||Differential Equations||Differential notation, separation of variables, rate calculations, exponential growth|
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