| topics | mathematical knowledge topics | mit ocw resources | readings | other resources |
|---|---|---|---|---|
Module 1: Control System Analysis | ||||
| 1. Course Introduction | ||||
| 2. Introduction to Control Systems | Functions | 18.013A: Readings Kleitman, Calculus with Applications, Chapter 1: Philosophy, Numbers and Functions | S: Sections 1.5-1.6: The Concept of a Function, Graphs of Functions | Kleitman, Calculus for Beginners and Artists, Chapter 3: Linear Functions |
| Linearization | 18.013A: Readings Kleitman, Calculus with Applications, Chapter 12: Applications of Differentiation: Direct Use of Linear Approximation | EP: Section 3.1: Introduction and Review of Power Series | Strang, Section 10.4: The Taylor Series for e^x, sin x, and cos x (PDF) | |
| First-Order Differential Equations | 18.03: Lecture Notes Linear Equations (Lec #3) (PDF) | EP: Section 1.5: Linear First-Order Equations S: Section 14.4: Taylor Series and Taylor's Formula | ||
| Laplace Transforms | 18.03: Lecture Notes Laplace Transform: Basic Properties (Lec #21) (PDF) 18.03: Readings Application to ODEs & Partial Fractions (Lec #22) (PDF) 18.03: Recitation Problems Laplace Transform & Poles (Recitation Problems #14) (PDF); Solutions (PDF) | EP: Chapter 4: Laplace Transform Methods | ||
| 3. Control System Analysis and Design | Functions | 18.013A: Readings Kleitman, Calculus with Applications, Chapter 1: Philosophy, Numbers and Functions | S: Sections 1.5-1.6: The Concept of a Function, Graphs of Functions | Kleitman, Calculus for Beginners and Artists, Chapter 3: Linear Functions |
| Second-Order Differential Equations | 18.03: Lecture Notes Solutions of Spring-mass-dashpot Models (Lec #9) (PDF) 18.03: Recitation Problems Second-order Linear Equations: Constant Coefficient, Homogeneous (Recitation Problems #6) (PDF); Solutions (PDF) | EP: Section 2.1: Second-Order Linear Equations | ||
| 4. Disturbances and Sensitivity | Functions | 18.013A: Readings Kleitman, Calculus with Applications, Chapter 1: Philosophy, Numbers and Functions | S: Sections 1.5-1.6: The Concept of a Function, Graphs of Functions | Kleitman, Calculus for Beginners and Artists, Chapter 3: Linear Functions |
| Differentiation | 18.013A: Readings Kleitman, Calculus with Applications, Chapter 8: Calculation of Derivatives by Rule | S: Chapters 2-4: The Derivative of a Function, The Computation of Derivatives, Applications of Derivatives | Strang, Chapter 2: Derivatives (PDF) Strang, Chapter 4: The Chain Rule (PDF) | |
| Partial Differentiation | Strang, Chapter 13: Partial Derivatives (PDF) | |||
| 5. Steady-State Errors | Functions | 18.013A: Readings Kleitman, Calculus with Applications, Chapter 1: Philosophy, Numbers and Functions | S: Chapter 19: Partial Derivatives | Strang, Chapter 13: Partial Derivatives (PDF) |
| Limits | S: Section 2.5: The Concept of Limit | Strang, Section 2.6: Limits (PDF) | ||
| 6. The s-Plane, Poles and Zeroes | Functions | 18.013A: Readings Kleitman, Calculus with Applications, Chapter 1: Philosophy, Numbers and Functions | S: Sections 1.5-1.6: The Concept of a Function, Graphs of Functions | Kleitman, Calculus for Beginners and Artists, Chapter 3: Linear Functions |
| Complex Numbers | 18.03: Readings Notes and Exercises C.1-C.3: Complex Numbers (Ses #5) (PDF) Supplementary Notes 5: The Algebra of Comlex Numbers (Ses #5) (PDF) Supplementary Notes 6: The Complex Exponential (Ses #5) (PDF) 18.03: Lecture Notes Complex Numbers, Complex Exponential (Ses #5) (PDF) | |||
| Partial Fractions | S: Section 10.6: The Method of Partial Fractions EP: Section 4.3: Translation and Partial Fractions | Strang, Section 7.4: Partial Fractions (PDF) | ||
| 7. Transient Response Characteristics and System Stability | Functions | 18.013A: Readings Kleitman, Calculus with Applications, Chapter 1: Philosophy, Numbers and Functions | S: Sections 1.5-1.6: The Concept of a Function, Graphs of Functions | Kleitman, Calculus for Beginners and Artists, Chapter 3: Linear Functions |
| Complex Numbers | 18.03: Readings Notes and Exercises C.1-C.3: Complex Numbers (Ses #5) (PDF) Supplementary Notes 5: The Algebra of Comlex Numbers (Ses #5) (PDF) Supplementary Notes 6: The Complex Exponential (Ses #5) (PDF) 18.03: Lecture Notes Complex Numbers, Complex Exponential (Ses #5) (PDF) | |||
| Partial Fractions | S: Section 10.6: The Method of Partial Fractions EP: Section 4.3: Translation and Partial Fractions | Strang, Section 7.4: Partial Fractions (PDF) | ||
| 8. Dominant Modes | Functions | 18.013A: Readings Kleitman, Calculus with Applications, Chapter 1: Philosophy, Numbers and Functions | S: Sections 1.5-1.6: The Concept of a Function, Graphs of Functions | Kleitman, Calculus for Beginners and Artists, Chapter 3: Linear Functions |
| Partial Fractions | S: Section 10.6: The Method of Partial Fractions EP: Section 4.3: Translation and Partial Fractions | Strang, Section 7.4: Partial Fractions (PDF) | ||
| 9. Transient Performance and the Effect of Zeroes | Functions | 18.013A: Readings Kleitman, Calculus with Applications, Chapter 1: Philosophy, Numbers and Functions | S: Sections 1.5-1.6: The Concept of a Function, Graphs of Functions | Kleitman, Calculus for Beginners and Artists, Chapter 3: Linear Functions |
| Linearization | 18.013A: Readings Kleitman, Calculus with Applications, Chapter 12: Applications of Differentiation: Direct Use of Linear Approximation | EP: Section 3.1: Introduction and Review of Power Series | Strang, Section 10.4: The Taylor Series for e^x, sin x, and cos x (PDF) | |
| Second-Order Differential Equations | 18.03: Lecture Notes Solutions of Spring-mass-dashpot Models (Lec #9) (PDF) 18.03: Recitation Problems Second-order Linear Equations: Constant Coefficient, Homogeneous (Recitation Problems #6) (PDF); Solutions (PDF) | EP: Section 2.1: Second-Order Linear Equations | ||
| 10. The Effect of Zeros | Functions | 18.013A: Readings Kleitman, Calculus with Applications, Chapter 1: Philosophy, Numbers and Functions | S: Sections 1.5-1.6: The Concept of a Function, Graphs of Functions | Kleitman, Calculus for Beginners and Artists, Chapter 3: Linear Functions |
| 11. State Space | Functions | 18.013A: Readings Kleitman, Calculus with Applications, Chapter 1: Philosophy, Numbers and Functions | S: Sections 1.5-1.6: The Concept of a Function, Graphs of Functions | Kleitman, Calculus for Beginners and Artists, Chapter 3: Linear Functions |
| First-Order Differential Equations | 18.03: Lecture Notes Linear Equations (Lec #3) (PDF) | EP: Section 1.5: Linear First-Order Equations S: Section 14.4: Taylor Series and Taylor's Formula | ||
| Second-Order Differential Equations | 18.03: Lecture Notes Solutions of Spring-mass-dashpot Models (Lec #9) (PDF) 18.03: Recitation Problems Second-order Linear Equations: Constant Coefficient, Homogeneous (Recitation Problems #6) (PDF); Solutions (PDF) | EP: Section 2.1: Second-Order Linear Equations | ||
| Vector-Matrix Equations | 18.03: Readings Notes and Exercises LS.1: Linear Systems (Ses #32) (PDF) 18.03: Lecture Notes Linear Systems and Matrices (Ses #32) (PDF) 18.03: Recitation Problems Systems of First-order Equations (Rec #21) (PDF); Solutions (PDF) Linear Systems (Rec #15) (PDF); Solutions (PDF) | EP: Section 5.3: Matrices and Linear Systems | Strang, Section 11.4: Matrices and Linear Equations (PDF) | |
| 12. State Space Modeling | Functions | 18.013A: Readings Kleitman, Calculus with Applications, Chapter 1: Philosophy, Numbers and Functions | S: Sections 1.5-1.6: The Concept of a Function, Graphs of Functions | Kleitman, Calculus for Beginners and Artists, Chapter 3: Linear Functions |
| Nth Order Differential Equations | EP: Section 2.2: General Solutions of Linear Equations | |||
| Vector-Matrix Equations | 18.03: Readings Notes and Exercises LS.1: Linear Systems (Ses #32) (PDF) 18.03: Lecture Notes Linear Systems and Matrices (Ses #32) (PDF) 18.03: Recitation Problems Systems of First-order Equations (Rec #21) (PDF); Solutions (PDF) Linear Systems (Rec #15) (PDF); Solutions (PDF) | EP: Section 5.3: Matrices and Linear Systems | Strang, Section 11.4: Matrices and Linear Equations (PDF) | |
| Second-Order Differential Equations | 18.03: Lecture Notes Solutions of Spring-mass-dashpot Models (Lec #9) (PDF) 18.03: Recitation Problems Second-order Linear Equations: Constant Coefficient, Homogeneous (Recitation Problems #6) (PDF); Solutions (PDF) | EP: Section 2.1: Second-Order Linear Equations | ||
| 13. More State Space Modeling and Transfer Function Matrices | Functions | 18.013A: Readings Kleitman, Calculus with Applications, Chapter 1: Philosophy, Numbers and Functions | S: Sections 1.5-1.6: The Concept of a Function, Graphs of Functions | Kleitman, Calculus for Beginners and Artists, Chapter 3: Linear Functions |
| Second-Order Differential Equations | 18.03: Lecture Notes Solutions of Spring-mass-dashpot Models (Lec #9) (PDF) 18.03: Recitation Problems Second-order Linear Equations: Constant Coefficient, Homogeneous (Recitation Problems #6) (PDF); Solutions (PDF) | EP: Section 2.1: Second-Order Linear Equations | ||
| Vector-Matrix Equations | 18.03: Readings Notes and Exercises LS.1: Linear Systems (Ses #32) (PDF) 18.03: Lecture Notes Linear Systems and Matrices (Ses #32) (PDF) 18.03: Recitation Problems Systems of First-order Equations (Rec #21) (PDF); Solutions (PDF) Linear Systems (Rec #15) (PDF); Solutions (PDF) | EP: Section 5.3: Matrices and Linear Systems | Strang, Section 11.4: Matrices and Linear Equations (PDF) | |
| Laplace Transforms | 18.03: Lecture Notes Laplace Transform: Basic Properties (Lec #21) (PDF) 18.03: Readings Application to ODEs & Partial Fractions (Lec #22) (PDF) 18.03: Recitation Problems Laplace Transform & Poles (Recitation Problems #14) (PDF); Solutions (PDF) | EP: Chapter 4: Laplace Transform Methods | ||
| Linear Algebra | 18.03: Readings Notes and Exercises LS.1: Review of Linear Algebra (PDF) | |||
| 14. Quanser Model and State Transition Matrices | Functions | 18.013A: Readings Kleitman, Calculus with Applications, Chapter 1: Philosophy, Numbers and Functions | S: Sections 1.5-1.6: The Concept of a Function, Graphs of Functions | Kleitman, Calculus for Beginners and Artists, Chapter 3: Linear Functions |
| Second-Order Differential Equations | 18.03: Lecture Notes Solutions of Spring-mass-dashpot Models (Lec #9) (PDF) 18.03: Recitation Problems Second-order Linear Equations: Constant Coefficient, Homogeneous (Recitation Problems #6) (PDF); Solutions (PDF) | EP: Section 2.1: Second-Order Linear Equations | ||
| First-Order Differential Equations | 18.03: Lecture Notes Linear Equations (Lec #3) (PDF) | EP: Section 1.5: Linear First-Order Equations S: Section 14.4: Taylor Series and Taylor's Formula | ||
| Linear Algebra | 18.03: Readings Notes and Exercises LS.1: Review of Linear Algebra (PDF) | |||
| Power Series | 18.03: Readings Notes and Exercises LS.6.3: The Exponential Matrix (PDF) | EP: Section 5.7: Matrix Exponentials and Linear Systems S: Chapter 14: Power Series | Strang, Section 10.5: Power Series (PDF) Kleitman, Calculus for Beginners and Artists, Section 15.5: Power Series | |
| Laplace Transforms | 18.03: Lecture Notes Laplace Transform: Basic Properties (Lec #21) (PDF) 18.03: Readings Application to ODEs & Partial Fractions (Lec #22) (PDF) 18.03: Recitation Problems Laplace Transform & Poles (Recitation Problems #14) (PDF); Solutions (PDF) | EP: Chapter 4: Laplace Transform Methods | ||
| 15. Solutions of State Space Differential Equations | First-Order Differential Equations | 18.03: Lecture Notes Linear Equations (Lec #3) (PDF) | EP: Section 1.5: Linear First-Order Equations S: Section 14.4: Taylor Series and Taylor's Formula | |
| Integration | E: Chapter 15: Vector Calculus S: Chapters 5,6,7,10 | Strang, Chapter 5: Integrals (PDF) Strang, Sections 15.1-15.2: Vector Fields, Line Integrals (PDF) | ||
| Convolution | 18.03: Readings Notes and Exercises I.4: Convolution (PDF) 18.03: Recitation Problems Impulse Response = Weight Function and Convolution (Rec #13) (PDF); Solutions (PDF) | EP: Section 4.4: Derivatives, Integrals, and Products of Transforms | ||
| Linear Algebra | 18.03: Readings Notes and Exercises LS.1: Review of Linear Algebra (PDF) | |||
| Inverse Laplace Transforms | 18.03: Lecture Notes Laplace Transform: Basic Properties (Lec #21) (PDF) 18.03: Readings Application to ODEs & Partial Fractions (Lec #22) (PDF) 18.03: Recitation Problems Laplace Transform & Poles (Recitation Problems #14) (PDF); Solutions (PDF) | EP: Chapter 4: Laplace Transform Methods | ||
| 16. Controllability | First-Order Differential Equations | 18.03: Lecture Notes Linear Equations (Lec #3) (PDF) | EP: Section 1.5: Linear First-Order Equations S: Section 14.4: Taylor Series and Taylor's Formula | |
| Power Series | 18.03: Readings Notes and Exercises LS.6.3: The Exponential Matrix (PDF) | EP: Section 5.7: Matrix Exponentials and Linear Systems S: Chapter 14: Power Series | Strang, Section 10.5: Power Series (PDF) Kleitman, Calculus for Beginners and Artists, Section 15.5: Power Series | |
| Linear Algebra | 18.03: Readings Notes and Exercises LS.1: Review of Linear Algebra (PDF) | |||
Table of Contents
Skills Review
Skills Review
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This section lays out, in a structured manner, the mathematics skills required of undergraduate students in 16.06.
Also provided is a table in which each mathematical knowledge topic is mapped to core courses within the Department of Aeronautics and Astronautics.
Readings listed in the table below are from the textbooks for 18.01, 18.02, and 18.03 and three online textbooks:
(S) Simmons, George F. Calculus with Analytic Geometry. 2nd ed. New York, NY: McGraw-Hill, 1995. ISBN: 0070576424.
(E) Edwards, C. Multivariable Calculus. 6th ed. Upper Saddle River, NJ: Prentice Hall, 2002. ISBN: 0130339679.
(EP) Edwards, C., and D. Penney. Elementary Differential Equations with Boundary Value Problems. 4th ed. Upper Saddle River, NJ: Prentice Hall, September 29, 1999. ISBN: 0130113018.
Online textbooks:
Strang, Gilbert. Calculus. Wellesley, MA: Wellesley-Cambridge Press, 1991. ISBN: 0961408820.
Kleitman, Daniel. Calculus for Beginners and Artists.
Kleitman, Daniel. Calculus with Applications. (used in 18.013A)
16.06 Skills Review
Further information on the Mathematical Knowledge Topics for each 16.06 lecture may be found in the Supplementary Math Notes (PDF), which are organized by 16.06 lecture topics and the associated Mathematical Knowledge Topics.
The following list of topics link to the corresponding entry in the table below.