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CAL 200

Introduction to Calculus for Beginners

Instructor

Dr. Garcia

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Course Overview

Introduction to Calculus for Beginners

Lesson 1: Understanding Limits

  • Objective: Introduce the concept of limits, explain their significance in calculus, and demonstrate basic limit problems.
  • Content: Definition of a limit, notation, finding limits from graphs and tables, basic limit laws.

Lesson 2: Continuity and Discontinuity

  • Objective: Explore the concept of continuity, identify types of discontinuities, and understand their impact on functions.
  • Content: Definition of continuity, types of discontinuities (removable, jump, infinite), examples, and exercises.

Lesson 3: The Derivative – Definition and Interpretation

  • Objective: Define the derivative, interpret it geometrically as the slope of a tangent line, and understand its physical meaning.
  • Content: Definition of the derivative, notation, the relationship between the derivative and the slope of a function, and basic differentiation rules.

Lesson 4: Techniques of Differentiation

  • Objective: Learn and apply various techniques for differentiating functions.
  • Content: Power rule, product rule, quotient rule, chain rule, and examples applying these techniques.

Lesson 5: Applications of Derivatives

  • Objective: Apply derivatives to solve real-world problems involving rates of change and motion.
  • Content: Problems involving velocity, acceleration, optimization, and related rates.

Lesson 6: Understanding Integrals

  • Objective: Introduce the concept of integration as the reverse process of differentiation.
  • Content: Definition of an integral, antiderivatives, basic integration rules, and indefinite integrals.

Lesson 7: The Definite Integral and Area Under a Curve

  • Objective: Understand the definite integral and its application in finding areas under curves.
  • Content: Definition of the definite integral, the Fundamental Theorem of Calculus, and calculating the area under a curve.

Lesson 8: Techniques of Integration

  • Objective: Learn various methods of integration to solve more complex problems.
  • Content: Integration by substitution, integration by parts, and the use of partial fractions.

Lesson 9: Applications of Integrals

  • Objective: Apply integrals to solve practical problems involving areas, volumes, and other quantities.
  • Content: Area between curves, volumes of solids of revolution (using disk and shell methods), and examples of physical applications.

Lesson 10: Introduction to Differential Equations

  • Objective: Introduce basic differential equations and their applications.
  • Content: Definition of a differential equation, basic solution techniques, and simple real-world applications such as population growth and cooling laws.

Each lesson should include a mix of theoretical explanations, practical examples, and exercises for students to practice and consolidate their understanding of the concepts.

  • Prerequisite(s):¬†MATH¬†105
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  • Last Update May 21, 2024