Problems in Calculus of One Variable

Categories: Grade 11 mathematics
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About Course

Calling all students!

This course provides an in-depth exploration of calculus problems as presented in the classic textbook by I.A. Maron, a revered resource in mathematical education. Designed for college students, this course focuses on solving a comprehensive array of problems, enabling a robust understanding of calculus of one variable.

Course Objectives:

  • To develop a thorough understanding of differential and integral calculus concepts.
  • To enhance problem-solving skills through systematic practice.
  • To prepare students for advanced courses in mathematics and related fields.

Course Benefits:

  1. Mastery of Fundamental Concepts: By working through the problems in I.A. Maron’s textbook, students will gain a solid grasp of the essential principles of calculus, including limits, derivatives, integrals, and their applications.
  2. Problem-Solving Skills: The course emphasizes a problem-solving approach, encouraging students to think critically and apply theoretical concepts to practical scenarios. This skill is invaluable not only in mathematics but also in various scientific and engineering disciplines.
  3. Preparation for Advanced Studies: A strong foundation in single-variable calculus is crucial for success in higher-level mathematics courses. This course equips students with the knowledge and skills necessary to excel in more complex areas of study.
  4. Confidence in Mathematical Abilities: Regular practice with a wide range of problems will build students’ confidence in their mathematical abilities, fostering a positive attitude towards tackling challenging problems.

✏️ Structured Learning: The course is structured to guide students through progressively challenging problems, ensuring a comprehensive understanding of each topic before moving on to the next.

⏱️ Detailed Solutions: Each problem is accompanied by detailed solutions, providing clear and concise explanations to aid understanding.

📕 Interactive Sessions: Engage in interactive sessions where complex problems are broken down step-by-step, and common pitfalls are addressed.

🧩 Assessment and Feedback:Regular assessments and constructive feedback help track progress and identify areas needing improvement.

By the end of this course, students will have a profound understanding of the calculus of one variable and the ability to apply their knowledge to solve complex mathematical problems. This course is an invaluable asset for any student aiming to excel in mathematics and related fields. ✨

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What Will You Learn?

  • Introduction to Mathematical Analysis
  • Differentiation of Functions
  • Applications of Differential Calculus to Investigation of Functions
  • Indefinite Integrals - basic Method of Integration
  • Basic Classes of Integrable Functions
  • The Definite Integral
  • Applications of the Definite integral
  • Improper Integrals

Course Content

Chapter 1: Introduction to Mathematical Analysis
Prerequisite to Calculus

  • 1.1. Real Numbers: The Absolute Value of a Real Number
  • 1.1.1 Exercise
  • 1.1.2 Exercise Solution
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