Math 311- Topics in Applied Mathematics I
Files
Below, please find links to helpful files, including the syllabus of the course. - Course syllabus
- Paper returning request Section 502 and Section 504
- Notes on Row Reduction (from Prof. Narcowich)
- Practice Exam I (from Prof. Yasskin): Do not solve exercise 7 (vector spaces is not including in our exam).
- Solutions to the Practice Exam I (from Prof. Yasskin)
- Review Homework for Midterm Exam 1(from Prof. de Wolff): No due; this homework is not mandatory. It is intended to help you to prepare yourself for the first midterm exam
- Solutions to the Review Homework for Midterm Exam 1 (from Prof. de Wolff)
- Definition and properties of vector spaces (from Prof. Yasskin)
- Notes on finding bases using row reduction (from Prof. Narcowich)
- Notes on Coordinates (from Prof. Narcowich)
- Notes on Changing Bases (from Prof. Narcowich)
- Review Homework for Midterm Exam 2 (from Prof. de Wolff): No due; this homework is not mandatory. It is intended to help you to prepare yourself for the second midterm exam
- Solutions to the Review Homework for Midterm Exam 2 (from Prof. de Wolff)
- Notes on Diagonalization (from Prof. Narcowich)
- Review Homework for the Final (from Prof. de Wolff): No due; this homework is not mandatory. It is intended to help you to prepare yourself for the final exam. It only cover the linear algebra topics.
Links Below, please find other helpful links.
Announcements
2016/12/08, 13:28 Please complete the evaluations. You can complete them in an electronic device of your choice (smartphone, laptop, or tablet). You open a browser and follow these three simple steps: Go to http://math.tamu.edu login with their NetID and password begin Deadline to complete an evaluation is 7:00am, Friday, December 9, 2016. I will really appreciate your feedback. Thank you for your time! Final exam on Friday December 09. Section 502: 12:30-2:30 pm at Blocker 149. Sectio 504: 3:00-5:00 pm at Blocker 121. Please bring your id. 2016/12/07, 13:15 Extra Office hours for the Final on Thursday December 08. 10:30-12:30 at Blocker 510A. 2016/12/05, 13:10 Homework about Vector Calculus is now available. No due date. From the textbook: Section 10.1 (page 674): 1, 2, 6, 8, 12, 16, 18, 20, 21, 24, 27, 30, 32. There are some nice problems of applications at the end of the section. Section 10.2 (page 684): 5, 7, 9, 10, 12, 14, 23, 25. Section 10.3 (page 696): 1, 3, 8, 13, 18, 20, 22, 24, 25, 27, 28, 32, 35. Lecture 12/01 Other formulation of line integrals (differential form). Reparametrization of a path. Relation between line integral and reparamentrizations. Green Theorem. Examples. Lecture 11/29 Orthogonality: Fundamental subspaces Theorem. Relation of nullspace and range of a matrix with orthogonal complements. Scalar and vector line integrals: definitions and examples. Lecture 11/22 Orthogonal complement. Orthogonal projection of a vector onto a subspace. Gram-Schmidt orthogonalization process. Orthonormalization process. Orthogonal/orthonormal basis. 2016/11/17, 17:20 Wednesday Office Hours (W 11/23) were rescheduled because of Thanksgiving break to Monday 11/21 from 1:15-2:15 pm. Only for this week! 2016/11/18, 17:50 Homework 10 now available. Due date: 12/01. Homework will be collected in the lecture. From the textbook: Section 5.1 (page 224): 3(b), 7, 17. If you want extra practice try 1(a), 1(d), 2(a), 2(d), 3(a), 3(c), 3(d), 13, 18. Section 5.2 (page 233): 1(b), 2(a), 3, 4, 6. If you want extra practice try 8, 9. Section 5.4 (page 252): 3, 7(a), 8, 14. If you want extra practice try 2, 4, 7(b), 7(c), 9, 10, 11, 13, 15, 20, 23, 26, 28, 30. Section 5.5 (page 269): 2, 6, 9. If you want extra practice try 4, 7, 8, 29(a), 29(b), 30(a), 30(b). Section 5.6 (page 280): 3, 4, 7. If you want extra practice try 1(a), 8. Lecture 11/17 Generalization of dot product: inner product. Definition and examples of inner product. Induced norm. Angle and orthogonality. Orthogonal and orthonormal sets. Orthogonality and linear independence. Lecture 11/15 Euclidean spaces: length, dot product, angle, distance. Generalization of length: norm. Examples. Lecture 11/10 Section 6.3: Basis of eigenvectors. Diagonalizable matrices. Examples. Lecture 11/08 Exam II. 2016/11/04, 15:20 Homework 9 now available. Due date: 11/17. Homework will be collected in the lecture. From the textbook: Section 6.1 (page 308): 1(a), 1(b), 1(f), 1(g), 1(h), 1(i), 1(l), 3, 4, 7, 9, 14, 28, 33. If you want extra practice try 1(c), 1(d), 1(e), 1(k), 8, 10, 11, 18. Section 6.3 (page 336): 1(a), 1(c), 1(d), 1(f), 2(a), 2(c), 2(d), 2(f), 3(a), 3(c), 3(d), 3(f) (items of Exercise 3, only if invertible), 4, 18 ( How are the eigenvalues and eigenvectors of B expressed in terms of those for A?). If you want extra practice try 1(b), 1(e), 2(b), 2(e), 3(b), 3(e) (items of Exercise 3, only if invertible), 5, 6, 29. 2016/11/03, 14:45 Exam II covers sections 3.1-6.1 (inclusive). It does not cover Chapter 5. Date: Tueday November 08, 2016. 2016/11/03, 14:45 Extra Office hours on Monday November 07. 11-12 at Blocker 510A. Lecture 11/03 Section 6.1: Eigenspaces of a matrix. Charactheristic equation and characteristic polynomial of a matrix. How to find the eigenvalues, eigenvectors and eigenspaces? Examples. Relation between the trace and the determinant of a matrix with its eigenvalues. Linear independence of eigenvectors of differents eigenvalues. Lecture 11/01 Section 4.3: Change of Basis of a linear operator. Examples. Similarity of matrices: definition and properties. Section 6.1: Eigenvalues and eigenvector of a matrix. Eigenspaces, characteristic polynomial, characteristic equation (Only section 502). How to find the eigenvalues? (Only section 502). 2016/10/27, 17:40 Homework 8 now available. Due date: 11/03. Homework will be collected in the lecture. From the textbook: Section 4.1-Part II (page 182): 13, 17, 19, 21, 22. If you want extra practice try 11, 14, 18, 23, 25. Section 4.2 (page 195): 2(a), 3(c), 4(c), 6, 8, 14, 15, 18. If you want extra practice try 7, 13, 16, 19, 20. Section 4.3 (page 202): 2, 4, 5, 6, 11, 15. If you want extra practice try 3, 7, 9, 12, 13, 14. Lecture 10/27 Section 4.1: Linear Tranformations: more examples and properties, Image and kernel: more examples and properties. Section 4.2: Matrix of a linear transformation. 2016/10/26, 14:50 Change on the date of Exam II: new date Tuesday November 08, 2016. Exam II was moved from Thursday November 01 to Tuesday November 08, 2016. The time and the room remain the same. Lecture 10/25 Section 3.6: Rank and nullity Theorem. Basis of the column space. Section 4.1: Linear Tranformations: definition, examples and properties. Image and kernel. 2016/10/21, 11:25 Homework 7 now available. Due date: 10/27. Homework will be collected in the lecture. From the textbook: Section 3.5 (page 159): 9. If you want extra practice try 10, 11. Section 3.6 (page 165): 1(c), 3, 4(b), 4(f), 8, 13, 18, 26. If you want extra practice try 1(b), 2(b), 4(d), 6, 7(a), 9, 10, 20, 22(a), 25. Section 4.1 - Part 1 (page 182): 1(e), 4, 5(c), 6(b), 6(d), 7(c), 7(d), 8 (b), 8(c), 9(a). If you want extra practice try 2, 5(b), 5(d), 6(a), 6(c), 8(a), 9(b), 9(c). Lecture 10/20 Section 3.5: Change of coordinates: general case, examples. Section 3.6: Row space and Column space: definition, examples and some properties. Linear systems and column space: consistency theorem. Rank and nullity Theorem (Section 502. Next class for Section 504). 2016/10/18, 14:05 Change on Homework 6. Due date: 03/03. Homework will be collected in the lecture. From the textbook: Due date: 10/20. Homework will be collected in the lecture. From the textbook: Section 3.4 (page 149): 2(b), 5, 7, 11, 12(f), 13, 16. If you want extra practice try 2(c), 2(f), 6, 8, 10, 12 14. Section 3.5 (page 159): 1(a), 2(a), 3(a), 5, 6. If you want extra practice try 1(b), 2(b), 3(b), 7. Exercises 9, 10 and 11 from Section 3.5 will be part of Homework 7. Lecture 10/18 Sections 3.5: Change of coordinates: case V = R^2. Coordinates, transition matrix, examples. 2016/10/18, 8:45 Today's Office Hours (T 10/18) were rescheduled from 1:20-2:20 pm (instead of the regular 1-2 pm time). Only for this week! 2016/10/14, 17:45 Homework 6 now available. Due date: 10/20. Homework will be collected in the lecture. From the textbook: Section 3.4 (page 149): 2(b), 5, 7, 11, 12(f), 13, 16. If you want extra practice try 2(c), 2(f), 6, 8, 10, 12 14. Section 3.5 (page 159): 1(a), 2(a), 3(a), 5, 6, 9. If you want extra practice try 1(b), 2(b), 3(b), 7, 10. Lecture 10/13 Sections 3.4: Basis: definition, standard basis and other examples, properties of basis. Dimension: definitions and first theorems. Lecture 10/11 Section 3.3: Linear independence: definition. Properties and examples. The Wronskian. Lecture 10/06 Section 3.2: Subspaces: definition, examples and properties. The null space of a matrix. The span of a set of vectors. Examples. 2016/10/06, 12:50 Homework 5 now available. Due date: 10/13. Homework will be collected in the lecture. From the textbook: Section 3.1 (page 122): 3, 4, 5, 10, 11, 12, 13, 16. If you want extra practice try 6, 7, 9, 14, 15 Section 3.2 (page 131): 1 (b), 1(c), 1(e), 2(a), 2(c), 2(d), 3(b), 3(c), 3(d), 3(f), 3(g), 4(a), 4(b), 5(b), 5(c), 6, 8, 13, 14, 16, 19, 21, 22. If you want extra practice try 1(d), 2(b), 3(e), 5(a), 5(d), 10, 11 (b), 11(d), 11(e), 12(b), 12(e), 15, 18, . Section 3.3 (page 143): 2(b), 2(c), 2(e), 3(b), 3(c), 3(e), 4(b), 5, 7, 8(a), 8(c), 9(a). 9(d), 14, 16, 17. If you want extra practice try 13, 15, 18, 20. Lecture 10/04 Sections 2.3: Cross product. Sections 3.1: Vector spaces: definition, properties and examples. 2016/10/04, 8:40 Today's Office Hours (T 10/04) were rescheduled from 1:35-2:35 pm (instead of the regular 1-2 pm time). Only for this week! Lecture 09/29 Exam I Exam I covers sections 1.1-2.3 (inclusive). 2016/09/27, 14:13 Extra Office hours on Tuesday September 27. 5-6 pm at Blocker 510A. Lecture 09/27 Sections 2.2: Properties of the determinant: relation with elementary row operations/matrices (Type I, II, and II), computing the determinant through row operations. Condition on the determinant for non-singularity. Determinant of the product of two matrices. Determinant of the inverse and of an scalar multiple of a matrix. Section 2.3: Cramer's rule. 2016/09/23, 11:55 Homework 4 now available. Due date: 10/06. Homework will be collected in the lecture. From the textbook: Section 1.5 (page 66): 10(b), 10(g), 12(a), 12(d). Section 2.1 (page 94): 1, 3(a), (c), (e), (g), 4, 6, 11. If you want extra practice try 3(b), 3(d), (f), (h), 7, 9. Section 2.2 (page 101): 1, 2, 3(c), 3(f), 4, 5, 6, 7, 9(c), 10. If you want extra practice try 3(d), 3(e), 8, 9(d), 9(e), 9(f), 14. Section 2.3 (page 109): 1(c), 2(b), 2(d). Lecture 09/22 Sections 1.5: Matrix Inversion. Compute the inverse using elementary row operations (first part). Sections 2.1: Definition of determinant: small cases, general cases: cofactor expansion. Determinant of the tanspose of a matrix, determinant of diagonal and triangular matrices. Sections 2.2: Properties of the determinant: relation with elementary row operations/matrices (Type I) 2016/09/20, 2:40 Change on Homework 3 The following exercises will be part of Homework 4 instead of Homework 3: Section 1.5 (page 66): 10(b), 10(g), 12(a), 12(d). 2016/09/20, 12:40 Wednesday Office Hours THIS week (W 09/21) were rescheduled from 9-10 am (instead of the regular 1:30-2:30 pm time). Only for this week! Lecture 09/20 Sections 1.5: Matrix Inversion, Inverse of diagonal matrices. Equivalent conditions for nonsingularity. Elementary matrices (and their inverses). Compute the inverse using elementary row operations (first part). 2016/09/15, 18:15 Homework 3 now available. Due date: 09/22. Homework will be collected in the lecture. From the textbook: Section 1.4 (page 56): 3, 4, 7, 9, 11(c), 11(f), 12, 13(c), 16, 20, 24(b), 27, 30. If you want extra practice try 1, 5, 6, 7, 8, 10(e), 10(f), 11(d), 17, 25, . Section 1.5 (page 66): 1, 5, 6, 9, 10(b), 10(g), 12(a), 12(d), 15, 18. If you want extra practice try 3(a), 7, 8, 10(c), 10(f), 13, 29. Lecture 09/15 Sections 1.4: Symmetric matrices. Matrix algebra: matrix multiplication, algebraic rules. Diagonal and triangular matrices. Operations of diagonal matrices. Identity matrix. Matrix Inversion. Lecture 09/13 Section 1.3: Matrix multiplication and linear systems (continuation), Consistency Theorem of Linear Systems. Matrix multiplication. Transpose matrix and properties. 2016/09/09, 19:40 Homework 2 now available. Due date: 09/15. Homework will be collected in the lecture. From the textbook: Section 1.2 (Applications - page 24): 15, 19, 21, 22(c). If you want extra practice try 18, 20, 22(a), 22(b). Section 1.3 (page 42): 1(c), 1(e), 1(f), 2(a), 2(b), 2(e), 2(f), 8(b), 9(a), 9(b), 10(a), 10(b), 13(a). If you want extra practice try 1(g), 1(h), 5, 6, 7, 8(c), 9(c), 10(c), 11, 12, 13(b). Lecture 09/08 Section 1.2: Parametric solutions. Applications of systems of linear equations (continuation). Section 1.3: Vectors, Matrix arithmetic: addition, scalar multiplication. Matrix multiplication and linear systems. Lecture 09/06 Section 1.2: Reduced Row Echelon Form, Consistency Check, Overdetermined/Underdetermined systems, Applications of systems of linear equations. Help Sessions has been schedule! Linear Algebra: Monday and Wednesday 7-9:30pm at Blocker 161. Lecture 09/01 Sections 1.1, 1.2: Equivalent systems, Elementary Operations, Matrix, Coefficient and Augmented matrix of a System, Elementary Row Operations, Row Echelon Form. 2016/9/2, 18:40 Homework 1 now available. Due date: 09/08. Homework will be collected in the lecture. From the textbook: Section 1.1 (page 10): 3(a), 3(d), 4, 5(b), 6(h), 8 (Use reduced row echelon form from Sec 1.2 instead of back substitution. Or try both ways.) and 9. If you want extra practice try 6(g), 7(Use reduced row echelon form from Sec 1.2 instead of back substitution. Or try both ways.), 10, 11. Section 1.2 - Part 1 (exercises about applications will be required later)(page 24): 3(b), 3(d), 5(e), 5(i), 6(b), 8, 10. If you want extra practice try 1 (b), 1(d), 1(g), 2(b), 2(e), 3(e), 5(f), 9. Lecture 08/30 Explanations of the course contents and syllabus. Section 1.1: Linear equation, system of linear equations, solutions of systems, 2x2 systems. |