Calendar · Lecture Notes
MIT OpenCourseWare
Advanced Calculus for Engineers
Art: Johannes Kepler, Konjukce Saturnu a Jupiteru Originál, 1596 · Public domain
- Instructors
- Dr. Dionisios Margetis, Prof. John W. M. Bush
- Term
- Fall 2004
- Level
- Graduate
- What's inside
- 1 lecture note · 1 reading · 71 other files · 4 web pages
- Materials open
- MIT OCW
About this course
Source: MIT OpenCourseWare 18.075 Advanced Calculus for Engineers, Fall 2004, Dr. Dionisios Margetis, Prof. John W. M. Bush — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.
Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.
Has MIT solutions
Before you start
Prerequisites are not listed here. Check MIT's own syllabus for this course.
How this course was organized
What's here, and what isn't
- A lecture sequence of 38 items is confirmed. Assignment and exam materials exist too, but MIT's own order for them could not be verified, so they're shown as materials below rather than a sequence.
Not included here
2 items from the source could not be safely included:
- Referenced in a table, but without MIT's own verified order, so it isn't used to claim a sequence. (2 items)
Materials by section
Grouped by section, as MIT organized them. Not sequenced or ordered.
Readings
- Evaluation of Real Definite Integrals (10.13) Handout 1 on Overview of Evaluation of (Real) Definite Integrals Download
- Singular Points of Linear Second-Order ODEs (4.3) The Method of Frobenius (4.4) Handout 2 on An Overview of the Fobenius Method Download
Lecture Notes
35 files
- Number Systems and Algebra of Complex Numbers Download
- Elementary Complex Functions, Part 1 Download
- Elementary Complex Functions, Part 2 Download
- Branch Points and Branch Cuts Download
- Analytic Functions Download
- Complex Integrals Download
- Cauchy’s Formula, Properties of Analytic Functions Download
- Taylor Series, Laurent Series Download
- Laurent Series (cont.) Download
- Properties of Laurent Series, Singularities Download
- Singularities (cont.) Download
- Residue Theorem Download
- Evaluation of Real Definite Integrals, Case I Download
- Evaluation of Real Definite Integrals, Case II Download
- Evaluation of Real Definite Integrals, Case III Download
- Evaluation of Real Definite Integrals, Case IV Download
- Theorems for Contour Integration Download
- Series and Convergence Download
- Ordinary Differential Equations Download
- Singular Points of Linear Second-order ODEs Download
- Frobenius Method Download
- Frobenius Method - Examples Download
- Frobenius Method (cont.) and a “particular type” of ODE Download
- Bessel Functions Download
- Properties of Bessel Functions Download
- Modified Bessel Functions Download
- Differential Equations Satisfied by Bessel Functions Download
- Introduction to Boundary-Value Problems Download
- Eigenvalues, Eigenfunctions, Orthogonality of Eigenfunctions Download
- Boundary Value Problems for Nonhomogeneous PDEs Download
- Sturm-Liouville Problem Download
- Fourier Series Download
- Fourier Sine and Cosine Series Download
- Complete Fourier Series Download
- Review of Boundary Value Problems for Nonhomogeneous PDEs Download
Assignments
11 files
- Chapter 10: 3, 4, 5, 9, 12, 13 Download
- Chapter 10: 33-38, 43, 44 Download
- Chapter 10: 48, 51, 52, 61, 62, 78-81 Download
- Chapter 10: 82, 88, 90, 91, 92 Download
- Chapter 10: 110, 111, 116 Download
- Chapter 4: 5(a-b), 6(a-e), 8, 11, 12 Download
- Chapter 4: 46-50 Download
- Chapter 5: 1-4 Download
- Chapter 5: 22-24, 31-34 Download
- Chapter 5: 36-38, 49, 50, 54, 55 [Please note: There are no solutions to 54, 55] Download
- Chapter 5: 58, 60, 61 Download
Exams
23 files
- Exam 1 · Practice Test I Download
- Exam 1 · Practice Test II Download
- Exam 1 · Practice Test I Solutions Download
- Exam 1 · Practice Test II Solutions Download
- Exam 1 Download
- Exam 1 · Exam solutions Download
- Exam 2 · Practice Test I Download
- Exam 2 · Practice Test II Download
- Exam 2 · Practice Test I Solutions Download
- Exam 2 · Practice Test II Solutions Download
- Exam 2 Download
- Exam 2 · Exam solutions Download
- Exam 3 · Practice Test I Download
- Exam 3 · Practice Test II Download
- Practice Test III Download
- Practice Test IV Download
- Exam 3 · Practice Test I Solutions Download
- Exam 3 · Practice Test II Solutions Download
- Practice Test III Solutions Download
- Errattum Practice Test III Solutions Download
- Practice Test IV Solutions Download
- Exam 3 Download
- Exam 3 · Exam solutions Download
Course outline
Calendar · Lecture Notes
Lecture 2: Elementary Complex Functions, Part 1
Calendar · Lecture Notes
Lecture 3: Elementary Complex Functions, Part 2
Calendar · Lecture Notes
Lecture 4: Branch Points and Branch Cuts
Calendar · Lecture Notes
Lecture 5: Analytic Functions
Calendar · Lecture Notes
Lecture 6: Complex Integrals
Calendar · Lecture Notes
Lecture 7: Cauchy’s Formula, Properties of Analytic Functions
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Lecture 8: Taylor Series, Laurent Series
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Lecture 9: Laurent Series (cont.)
Calendar · Lecture Notes
Lecture 10: Properties of Laurent Series, Singularities
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Lecture 11: Singularities (cont.)
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Lecture 12: Residue Theorem
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Lecture 13: In-class exam 1
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Lecture 14: Evaluation of Real Definite Integrals, Case I
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Lecture 15: Evaluation of Real Definite Integrals, Case II
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Lecture 16: Evaluation of Real Definite Integrals, Case III
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Lecture 17: Evaluation of Real Definite Integrals, Case IV
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Lecture 18: Theorems for Contour Integration
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Lecture 19: Series and Convergence
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Lecture 20: Ordinary Differential Equations
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Lecture 21: Singular Points of Linear Second-Order ODEs
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Lecture 22: Frobenius Method
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Lecture 23: Frobenius Method - Examples
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Lecture 24: Frobenius Method (cont.) and a “particular type” of ODE
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Lecture 25: Bessel Functions
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Lecture 26: Properties of Bessel Functions
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Lecture 27: Modified Bessel Functions
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Lecture 28: In-class exam 2
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Lecture 29: Differential Equations Satisfied by Bessel Functions
Calendar · Lecture Notes
Lecture 30: Introduction to Boundary-Value Problems
Calendar · Lecture Notes
Lecture 31: Eigenvalues, Eigenfunctions, Orthogonality of Eigenfunctions
Calendar · Lecture Notes
Lecture 32: Boundary Value Problems for Nonhomogeneous PDEs
Calendar · Lecture Notes
Lecture 33: Sturm-Liouville Problem
Calendar · Lecture Notes
Lecture 34: Fourier Series
Calendar · Lecture Notes
Lecture 35: Fourier Sine and Cosine Series
Calendar · Lecture Notes
Lecture 36: Complete Fourier Series
Calendar · Lecture Notes
Lecture 37: Review of Boundary Value Problems for Nonhomogeneous PDEs
Calendar · Lecture Notes
Lecture 38: In-class exam 3
MIT OpenCourseWare, Dr. Dionisios Margetis, Prof. John W. M. Bush, 18.075 Advanced Calculus for Engineers, Fall 2004.
License: CC BY-NC-SA 4.0 · Edition: Fall 2004 · Open the original course on OCW ↗
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