Calculus 101 - Single Variable Calculus

This is the first of three courses in the basic calculus sequence taken primarily by students in science, engineering, and mathematics. topics include the limit of a function, the derivative of algebraic, trigonometric, exponential, and logarithmic functions, and the definite integral and its basic applications to area problems. applications of the derivative are covered in detail, including approximations of error using differentials, maximum and minimum problems, and curve sketching using calculus.

Pre-requisite course in general for all core mathematics courses in high school with a minimum Algebra 1, Geometry, and Algebra II with an appropriate mathematics placement score. An Alternative to this is that the student should successfully pass with Pre-Calculus.

00 - Pilot

Course : Calculus 101

Features : Lecture Notes, Lecture PPT, Related video link, Suggested Experiment

Course Meeting Time:

Discussion : 2 sessions / week, 1 hour / session

Recitation : 1 session / week, 1 hour / session

Pre-requisite:

Calculus 101 is a first year, first semester course at AT.LS. The pre-requisites are high school algebra 1, algebra 2, geometry, and pre-calculus. Prior experience with calculus is helpful but not essential.

Course Descriptions:

Calculus is a foundational course in Science. It plays an important role in the understanding of Science, Technology, Engineering, Economics, and Mathematics among other disciplines. This introductory Calculus course is designed to give you the conceptual idea and understanding differentiation and integration of functions of one variable, with applications, on typed of topics like:

  • Concepts of Function, Limits, and Continuity

  • Differentiation: rules, graphing, rates, approximations.

  • Definite and Indefinite Integration

  • The Fundamental Theorem of Calculus

  • Application of Geometry in Integral: Area, Volume, Arc of Length

  • Technique of Integration

  • Approximation of Definite Integral, Improper Integrals, and L’Hôspital’s Rule

The course is designed for Calculus enthusiast in all levels, beginner, intermediate, expert, who want to understand the conceptual laws and physical processes that govern the sources, extraction, transmissions, storage, conversion, and end uses of Calculus.

Course Goal:

The basic objective of Calculus is to relate small-scale quantities to large-scale quantities. This is accomplished by means of the Fundamental Theorem of Calculus. After completing this course, learner will able to demonstrate an understanding of the large-scale as a cumulative sum, of the small-scale as a rate of change, and of the inverse relationship between them, and competency in:

  1. Use both the definition of limit, definition and rules of differentiation to differentiate function or as a limits.

  2. Sketch the graph of a function using asymptotes, critical points, the derivative test for increasing/decreasing functions, and concavity.

  3. Apply and setup differentiation to solve applied Max/min problems.

  4. Apply and setup differentiation to solve related rates problems.

  5. Evaluate integrals both by using Riemann Sums and by using the Fundamental Theorem of Calculus.

  6. Apply integration to compute volumes by slicing, arc lengths, Volumes of Revolution and Surface Areas of Revolution.

  7. Evaluate integrals technique, such as substitution, inverse substitution, partial fractions and integration by parts.

  8. Setup and solve 1st order differential equations (ODE)

  9. Use L’Hospital’s rule to evaluate certain indefinite forms.

  10. Determine convergence/divergence of improper integrals and evaluate convergent improper integrals.

  11. Estimate and compare series and integrals to determine convergence.

  12. Find the Taylor series expansion of a function near a point.

Course Structure:

This course, designed for independent study, has been organized to follow the sequence of topics covered in learning course on Calculus for Beginner. The content is organized into five main major units:

  1. Functions

  2. Limits

  3. Differentiation

  4. Integration

  5. Exploring the Infinite

Each of units has been further divided into parts (A, B, C, etc.) with each part containing a sequence of sessions. Because each session builds on knowledge from previous sessions, it’s important you progress through the sessions in order. Each session covers an amount you might expect to complete in one week.

Within each unit you will be presented with sets of problems at strategic points, so you can test your understanding of the material. As you begin each part of a unit, review the problem set at its end so that you may work toward solving those problems as you learn new material.

AT.LS expects its learner to spend about 100 hours on this course. More than half of that time is spent preparing for class and doing assignments. It’s difficult to estimate how long it will take you to complete the course, but you can probably expect to spend an hour or more working through each individual session.

Lecture PPT:

Most sessions include ppt and hopefully an audio from lectures of Albert Tan teaching Calculus, recorded live on the office room in the spring of 2020. The PPT was carefully segmented to take you step-by-step through the content. The PPT are accompanied by supporting course notes, and audio.

Recitation PPT:

This course includes a dozen of recitation PPT – brief problem solving sessions taught by an experienced learner – developed and recorded especially for you, the independent learner.

Readings and Assignments:

No special textbook is required for this course, but there's a suggestion textbook as shown in textbook section.

The notes that accompany the PPT present their content slightly more formally than lecture does. If you wondering exactly what conditions must hold for a statement to be true or if you wish to see the details of the calculations displayed on the slides, check the notes.

“Worked Examples” present a problem or problems to be solved; many of these problems have appeared on homework assignments at course. After you have solved these problems you can check your answer against a detailed solution.

Some worked examples will be accompanied by a Mathletes. These interactive learning tools will improve your geometric intuition and illustrate how changes in certain factors affect the results of different calculations.

Problem sets occur at the end of each part; these were taken directly from homework assigned at each course. As you start each part, familiarize yourself with the problems in the problem set. This will enable you to work on each problem as you gain the knowledge you need to solve it. Once you have completed the problem set you can check your answers against the solutions provided. (The problem sets are carefully selected from a longer list of questions available to you. Do not hesitate to work any problem that piques your interest).

Textbook:

  1. Jr, George B. Thomas. Thoma’s Calculus 13th Ed. Published by Pearson. ISBN: 978-0-321-87896-0

  2. Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey. Calculus with Applications 11th Ed. Published by Pearson. ISBN: 978-1-292-10897-1

This course is self-contained and no textbook is required. If you have access to a Calculus text, it will probably serve as a useful companion to this course, although you might have to deal with slight differences in terminology and notation.

Homework and Exams:

There will be 8 problem sets, due on Fridays of a week. You may turn in one problem set late with no penalty, provided you do so before solutions are given out. Partial credit may be awarded for subsequent late homework, but you must talk with your instructor.

There will be 5 in-class 50 minutes exams during the lecture hour. There will also be one three-hour final exam during finals week. The-in class exams and the final exam are open book and calculators are allowed. You will be allowed to use both sides of a index card.

Each unit ends in an exam. To prepare for exam, check that you are proficient in each of the topics listed in the exam review lecture and review your work on the unit’s examples and problem sets. Allow yourself one hour to work each exam and three hours to complete the final. The exams are quiet challenging; do not be surprised if you are unable to complete all of the questions correctly in the time allowed.

Make-up Exams:

If you miss or fail an exam, you make take a make-up exam at certain arranged times. You will be notified by an e-mail soon after taking an exam if you have failed it, so that you can plan for the make-up. make ups for failed exams can boost your grade only up to the lowest passing score (C-), which will be announced. Make-ups for full credit are permitted with a medical excuse. If you must be absent for other reasons, such as team sports, you must arrange to be excused in advance.

Grading:

Activities Problem

Eight Problem Sets

Final Standardization

Outline:

Chapter 1 – Functions

Chapter 2 – Limits

Chapter 3 – Derivative

Chapter 4 – Application of Derivative

Additional Comment:

This course includes features that do not display correctly in random browser. For best results, I would like to recommend viewing this course with the latest Microsoft Edge, Mozilla Firefox, or Google Chrome.