Advanced Calculus: Differentiation to Differential Equations
Master advanced calculus concepts: series, integration techniques, and differential equations. Perfect for STEM students and professionals.
Master advanced calculus concepts: series, integration techniques, and differential equations. Perfect for STEM students and professionals.
This comprehensive course delves into advanced calculus concepts, building upon foundational knowledge to explore complex mathematical principles. Designed for intermediate-level learners, the course covers key topics such as advanced differentiation techniques, integration methods, series representations of functions, and an introduction to differential equations. Through four engaging modules, students will develop crucial mathematical skills applicable to various fields in science, engineering, and commerce. The course balances theoretical understanding with practical applications, ensuring a thorough grasp of advanced calculus principles and their relevance in solving real-world problems.
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What you'll learn
Master advanced differentiation techniques including L'Hopital's Rule and Newton's Method
Develop proficiency in complex integration methods such as integration by parts and partial fractions
Understand and apply series representations of functions, including Taylor and Maclaurin series
Gain competence in solving basic differential equations and understanding their applications
Apply advanced calculus concepts to real-world problems in science and engineering
Enhance mathematical reasoning and proof techniques in the context of advanced calculus
Skills you'll gain
This course includes:
13.6 Hours PreRecorded video
28 assignments
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FullTime access
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There are 4 modules in this course
This comprehensive advanced calculus course builds upon fundamental calculus concepts to explore more complex mathematical principles and techniques. The curriculum is structured to provide a deep understanding of advanced differentiation and integration methods, series representations of functions, and an introduction to differential equations. Students will explore applications in various fields, including physics, engineering, and mathematical modeling. The course emphasizes both theoretical foundations and practical problem-solving skills, preparing learners for advanced studies in mathematics and its applications in science and technology.
Differentiation
Module 1 · 9 Hours to complete
Integration
Module 2 · 13 Hours to complete
Series Representations of Functions
Module 3 · 8 Hours to complete
Introduction to Differential Equations
Module 4 · 8 Hours to complete
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Instructor
Advancing Mathematics Education and Research
David Easdown is an Associate Professor of Mathematics at the University of Sydney's School of Mathematics and Statistics, within the Faculty of Science. He is dedicated to developing undergraduate mathematics courses across all years and levels, with a recent focus on bridging secondary and tertiary education. Actively supervising honours and postgraduate students in various topics related to pure mathematics and mathematics education, David's primary research interests include algebra and mathematics education. His latest algebra research delves into permutation group theory and combinatorial semigroup theory. In mathematics education, he investigates the applications of threshold concepts and the SOLO taxonomy to design and implement innovative assessment methods. David has published extensively, including his widely used textbook, A First Course in Linear Algebra, available through Pearson Education Australia, which serves students both in Australia and internationally.
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