Calculus of One Real Variable
This course intends to develop a thorough understanding of the fundamental aspects of calculus of a single variable which is a fundamental tool in Sciences, Engineering and Economics.
Evaluating Limits
Explore the concept of limits in calculus, covering definitions, asymptotes, limit laws, continuity, and the Intermediate Value Theorem through practical examples and theorems.
Limits and Continuity
Explore epsilon-delta continuity, uniform continuity, and limits through examples and theorems. Develop a deep understanding of fundamental calculus concepts and their applications.
Graph, Limits, & Continuity
Explore limits, continuity, and the Intermediate Value Theorem. Learn to find function domains for rational, square root, and logarithmic functions through practical examples.
Polynomials
Comprehensive guide to polynomials covering characteristics, binomial expansion, real, irrational, and complex zeros. Includes practical examples and step-by-step solutions for various polynomial-related problems.
What Numbers Satisfy This Inequality? - IMO 1962 Problem 2
Detailed solution to IMO 1962 Problem 2, exploring a complex square root inequality through mathematical analysis, intermediate value theorem, and algebraic manipulation.
AP Calculus AB and BC - Unit 1 Review - Limits and Continuity
Comprehensive review of limits and continuity for AP Calculus AB/BC, covering key concepts, theorems, and problem-solving techniques with clear explanations and examples.
Characteristics of Polynomials - Polynomials - Pre-Calculus
Explore zeros, multiplicity, and end behavior of polynomials in factored form. Learn to sketch polynomial graphs using these characteristics and the Intermediate Value Theorem.
Limits and Continuity
Practice multiple-choice problems on limits and continuity, covering factoring, rational functions, radicals, trigonometry, asymptotes, theorems, and piecewise functions for a comprehensive calculus review.
Sam Sanders - Uniformity in Mathematics
Explore uniformity in mathematics, from historical examples to modern applications. Examine how uniform theorems challenge traditional logical systems and impact proof methods across various mathematical domains.
Difficulties with Real Numbers as Infinite Decimals - Part 1
Explores challenges in defining real numbers as infinite decimals, examining advantages and drawbacks of the infinite choice approach, and discussing historical debates on arithmetic laws and mathematical foundations.
AP Calculus AB and BC Free Response Questions Review - 55 Problems
Comprehensive review of AP Calculus AB/BC topics through 55 free-response questions, offering in-depth solutions and exam preparation for advanced mathematics students.