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US$15
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Duration: 6 Months
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Delivery mode: Online
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Group size: Individual
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Instruction language:
English,
Urdu
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Certificate provided:
No
Welcome to our comprehensive Calculus I and II course, designed to provide a solid foundation in the fundamental concepts of calculus. Whether you are a high school student preparing for college-level mathematics or a college student seeking to strengthen your understanding, this course will equip you with the necessary skills and knowledge to succeed.
Calculus I:
Calculus I introduces the basic concepts of calculus, focusing on limits, derivatives, and integrals of single-variable functions. Key topics include:
Limits and Continuity: Understanding the behavior of functions as they approach specific points or infinity.
Derivatives: Learning how to compute the derivative of a function, interpret its meaning, and apply it to real-world problems.
Applications of Derivatives: Exploring practical applications such as optimization, motion, and related rates.
Integrals: Introduction to definite and indefinite integrals, the Fundamental Theorem of Calculus, and basic integration techniques.
Applications of Integrals: Utilizing integrals to solve problems involving area, volume, and accumulation.
Calculus II:
Building on the foundation of Calculus I, Calculus II delves deeper into advanced integration techniques, series, and multivariable functions. Key topics include:
Advanced Integration Techniques: Mastering methods such as integration by parts, trigonometric integrals, partial fractions, and improper integrals.
Applications of Integration: Applying integration to more complex problems in physics, engineering, and economics.
Sequences and Series: Understanding the convergence and divergence of sequences and series, including power series and Taylor series.
Parametric Equations and Polar Coordinates: Analyzing curves described by parametric equations and polar coordinates.
Introduction to Multivariable Calculus: Exploring partial derivatives, multiple integrals, and vector calculus.
Throughout the course, students will engage with a variety of problems and applications to develop a deep understanding of calculus concepts. With a balance of theoretical knowledge and practical skills, this course is essential for anyone pursuing studies in mathematics, science, engineering, or related fields.