This course is based on the book entitled “Basic Training in Mathematics” written by Prof. R. Shankar at Yale. The course is designed in response to the frequent need of materials science and engineering (MSE) students to apply basic math to their own research. The course covers fundamental topics in calculus, power series, and differential equations. It presents each topic in its simplest form but ensures a thorough treatment, allowing MSE students—and anyone in the physical sciences—to build a strong mathematical foundation.
Intended as a 6-week undergraduate-graduate course, the course offers an approach that MSE department might consider to better prepare students for advanced science studies. It is structured for self-study, addressing common student questions directly, making it a resource for both structured and independent learning. This early investment in mathematical preparation helps foster success in the materials science and engineering, where proficiency in mathematics can significantly impact future achievements.
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5个视频1篇阅读材料1个作业
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5个视频•总计139分钟
1-1 Introduction•27分钟
1-2 Exponential Fuction•26分钟
1-3 Log Functions•38分钟
1-4 Application of Calculus•18分钟
1-5•30分钟
1篇阅读材料•总计10分钟
Week 1 Lecture Note•10分钟
1个作业•总计30分钟
Differential Calculus of One Variable - Graded Quiz•30分钟
Integral Calculus
第 2 单元•小时 后完成
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5个视频1篇阅读材料1个作业
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5个视频•总计78分钟
2-1 Basics of Integration•10分钟
2-2 Different Ways of Integration•14分钟
2-3 Integration by Parts•18分钟
2-4 Change of Variable•18分钟
2-5 Differentiating with Respect to a Parameter•18分钟
1篇阅读材料•总计10分钟
Week 2 Lecture Note•10分钟
1个作业•总计30分钟
Integral Calculus - Graded Quiz•30分钟
Calculus of Many Variables
第 3 单元•小时 后完成
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5个视频3篇阅读材料1个作业
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5个视频•总计75分钟
3-1 Maxima and Minima•19分钟
3-2 Lagrange Multiplier•17分钟
Statistical Mechanics Interlude•21分钟
3-4 Integral Calculus of Many Variables 2•8分钟
3-5•10分钟
3篇阅读材料•总计30分钟
Lecture Notes: Lagrange Multiplier•10分钟
Lecture Notes•10分钟
Week 3 Lecture Note•10分钟
1个作业•总计30分钟
Calculus of Many Variables - Graded Quiz•30分钟
Applied Math for Materials Science and Engineering (Part 1) Final Exam
The Korea Advanced Institute of Science and Technology (KAIST) was established in 1971 by the Korean government as the nation’s first research-intensive graduate school for science, engineering and technology. It has now grown into one of the world’s best universities, delivering top notch education and research programs for undergraduate and graduate students. KAIST encourages interdisciplinary and convergent research across a wide spectrum of disciplines, as well as strong collaborations with industry and global institutions.
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Korea Advanced Institute of Science and Technology(KAIST)
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