INTRODUCTION TO CALCULUS COURSE 2 ONLINE COURSE CREATED

INTRODUCTION TO CALCULUS COURSE 2 ONLINE COURSE CREATED BY THI NANCY PHAM DATE CREATED 06/11/2020

COURSE OVERVIEWS • This second course covers the second fundamental principal of Calculus which is Integrations (Anti-Derivatives). • Topics includes: Differential Equations; Problems involving Motions; The Laws of Natural Growth; Logistic Equations; Sum of the Natural Numbers; Sum of the Squares of Natural Numbers; Sum of Cubes of Natural Numbers with all their Proofs. ; That led to Areas Under the Curves; Integral Calculus which is also the second fundamental principal of Calculus that involving The Substitution Rules for indefinite Integrals (the antiderivatives); Integrations by Parts; Partial fractions; Trigonometric Substitutions; Volumes of Revolutions; Polar Coordinates. • The content of this course is equivalent to the content of the first course in Calculus in University. This course was tailored with details and in adeptness.

Chapter 1 - Differential Equations Lesson 1: Antiderivatives In the first course, we have learned Derivatives (going forward), in this second course, we now will learned (going backward) Antiderivatives. Lesson 2 : Problems involving Motion Lesson 3: Newton’s Laws of Cooling Lesson 4: The Logistic Equation Lesson 5: Second Order of Differential Equation. Chapter 1 Quiz

Add a Slide Title - 2 Chapter 2 – Proofs of Series and Sigma Notation Areas Under The Curves and Integrations. • Lesson 1: Sigma Notation and Basic Properties. • Lesson 4: Integration Notation and Areas Under the Curves • Lesson 2: Proof of the natural number and the Squares of Natural Number • Lesson 5: Areas Between Curves • Lesson 3: Proof of the Sum of Natural Cube.

Chapter 3 - Definite Integrals and Indefinite Integrals Lesson 1: Areas as limits- Riemann Sum Approximation. Lesson 2: The Definite Integral Lesson 3: The Fundamental Theorem of Calculus Lesson 4: Properties of Integrals.

• Lesson 1: Cumulative Review • Lesson 2: The Substitution Rules • Lesson 3: Integration by parts Chapter 4 Methods of Integrations Chapter 4: The Substitution Rules Integration by Parts Trigonometric Substitution • Lesson 4: Trigonometric Subtitutions

Chapter 5: Volumes of Solid Revolutions The Disk Method The Washer Method The Shell Methods Lessson 1: Volumes of Solid Revolution – The Disk Method Lesson 2: The Washer Method Lesson 3: The Shell Method

Chapter 6 (Additional Lesson) Polar Coordinates Understand sketch Polar Coordinates.

Review Cumulative Exams – Practice Exam Register for Final Examination.