Calculus Syllabus Resource & Lesson Plans
 Course type: Selfpaced
 Available Lessons: 105
 Average Lesson Length: 8 min

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chapter 1 / lesson 1What is a Function: Basics and Key Terms
Course Summary
This 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.to start this course today
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13 chapters in Calculus Syllabus Resource & Lesson Plans
Course Practice Test
Check your knowledge of this course with a 50question 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 bitesized chunks. These lessons cover single topics like 1sided 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.
Video Lessons
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 jumpingoff 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.
Transcripts
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.
Quizzes
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  Jumpstart a discussion with questions like: What are some of the applications of the intermediate value theorem?
Sample Syllabus
Below is a sketch of the calculus syllabus modeled on a 13week 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, pointslope 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, 1sided 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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