Math 311- Topics in Applied Mathematics I
Files
Below, please find links to helpful files, including the syllabus of the course. - Course syllabus
- Notes on Row Reduction (from Prof. Narcowich)
- Paper returning request
- Definition and properties of vector spaces (from Prof. Yasskin)
- Practice Exam I (from Prof. Yasskin)
- Solutions to the Practice Exam I (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)
- Notes on Diagonalization (from Prof. Narcowich)
Links Below, please find other helpful links.
Announcements
2016/4/29, 18:15 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 I will really appreciate your feedback. Thank you for your time! 2016/4/28, 17:35 Review for the final Wednesday May 04, 10:30 am to 12:30 pm at Blocker 605AX. 2016/4/28, 17:25 Office hours for the final Monday May 02, 11:30 am to 12:30 pm at Blocker 509A Tuesday May 03, 1 to 2 pm at Blocker 509A 2016/4/27, 12:25 Remember Exam III: Thursday April 28. The time and the room remain the same: 9:35-10:50 am at CHEN 112. Homework 10 now available. Due date: 04/21. Homework will be collected in the lecture. From the textbook: Section 5.1 (page 224): 3(b), 3(d), 7, 17, 18. If you want extra practice try 1(a), 1(d), 2(a), 2(d), 3(a), 3(c), 13. Section 5.2 (page 233): 2(a), 4. If you want extra practice try 1(b), 3, 6, 9. Section 5.4 (page 252): 3, 7(a), 8, 14. If you want extra practice try 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, 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. 2016/4/21, 11:35 Extra office hours on Monday April 25. 3-4 pm at Blocker 509A. Lecture 04/21 Orthogonal complement: definition, properties, examples. Fundamental subspaces: N(A), R(A). Gram-Schmidt orthogonalization process. Normalization. Lecture 04/19 Inner product: definition and examples. Induced norm. Angle. Orthogonality. Relation with linear independence. Orthogonal projection. Lecture 04/14 Euclidean spaces. Generalization of length: norm. Generalization of dot product: inner product. Lecture 04/12 Quiz. Section 6.3: Basis of eigenvectors. Diagonalizable matrices. Diagonalizable linear operators. Examples. 2016/4/12, 16:25 Change on the date of Exam III: new date Tuesday April 26. Exam III was moved form Thursday April 21 to Tuesday April 26. The time and the room remain the same: 9:35-10:50 am at CHEN 112. 2016/4/12, 16:20 Homework 9 now available. Due date: 04/14. 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. Lecture 04/07 Section 6.1: Eigenspaces of a matrix. Charactheristic equation and characteristic polynomial of a matrix. How to find the eigenvalues and eigenvectors? Examples. Eigenvalues, eigenvectors, characteristic polynomial and characteristic equation of a linear operator. Relation with the eigenvectors and eignevalues of a matrix of the linear transformation. Linear independence of eigenvectors of differents eigenvalues. Lecture 04/05 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. Lecture 03/31 Section 4.2: Matrix of a linear transformation: general case. Section 4.3: Change of basis of a linear operator. 2016/2/17, 16:25 Exam II covers sections 3.1-4.1 (inclusive) and also the Theorem (matrix of a linear transformation) of section 4.2 that we discussed on the lecture of March 24. Date: Tueday Mar 29, 9:35-10:50 am at CHEN 112. 2016/3/25, 16:20 Homework 8 now available. Due date: 04/05. Homework will be collected in the lecture. From the textbook: Section 4.1 (page 182): 1(e), 4, 5(c), 6(b), 6(d), 7(c), 7(d), 8, 11, 13, 17, 19, 21, 22. If you want extra practice try 9, 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, 20. Section 4.3 (page 202): 2(a), 2(b), 4, 5, 6, 11, 15. If you want extra practice try 3, 7, 9, 13. 2016/3/25, 16:15 Extra Office hours on Monday March 28. 10-11 am at Blocker 509A. Lecture 03/24 Section 4.1: Linear Tranformations, Image and kernel: more examples and properties. Section 4.2: Matrix of a linear transformation. Lecture 03/22 Section 3.6: Linear systems and column space: consistency theorem. Basis of the column space. Section 4.1: Linear Tranformations: definition, examples and properties. Image and kernel. 2016/3/11, 15:25 Homework 7 now available. Due date: 03/24. Homework will be collected in the lecture. From the textbook: 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. Section 3.6 (page 165): 1(c), 3, 4(b), 8, 13, 18, 26. If you want extra practice try 2(b), 4(d), 6, 7(a), 9, 10, 20, 22(a), 25. 2016/3/10, 16:50 Change on the date of Exam II: new date Tuesday March 29. Exam II was moved form Thursday March 24 to Tuesday March 29. The time and the room remain the same: 9:35-10:50 am at CHEN 112. Lecture 03/10 Section 3.5: Change of coordinates: general case, examples. Section 3.6: Row space and Column space: definition, examples and some properties. Rank and nullity Theorem. Lecture 03/08 Section 3.4: Basis and dimension: more theorems, standard basis. Sections 3.5: Change of coordinates: case V = R^2. Coordinates, transition matrix, examples. Lecture 03/03 Section 3.3: Linear independence: the Wronskian. Sections 3.4: Basis and dimension: definition, examples and first theorems. Lecture 03/01 Section 3.2: Subspaces: more examples. Section 3.3: Linear independence: definition. Properties and examples. Lecture 02/25 Section 3.2: Subspaces: definition, examples and properties. The null space of a matrix. The span of a set of vectors. Examples. 2016/2/25, 13:45 Homework 6 now available. Due date: 03/10. Homework will be collected in the lecture. From the textbook: 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. Section 3.4 (page 149): 2(b), 2(c), 2(e), 5, 7, 11, 12, 13, 16. If you want extra practice try 6, 8, 10, 14. 2016/2/25, 13:40 Change on Homework 5. Due date: 03/03. Homework will be collected in the lecture. From the textbook: Section 3.1 (page 122): 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16. Section 3.2 (page 131): 1 (b), 1(c), 1(d), 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 10, 11 (b), 11(d), 11(e). Sections 3.3 and 3.4 will be on Homework 6. 2016/2/25, 13:35 Office Hours are cancelled next week (T 03/01 and W 03/02). Lectures are normal next week (T 03/01 and R 03/03). Lecture 02/23 Exam I. Lecture 02/18 Practice for Exam I. Sections 3.1: Vector spaces: more examples and some properties. 2016/2/19, 12:35 Office hours on Monday Feb 22. 9-10 am at Blocker 509A. 2016/2/17, 16:35 Exam I covers sections 1.1-3.1 (inclusive). Date: Tueday Feb 23, 9:35-10:50 am at CHEN 112. 2016/2/16, 16:50 Homework 5 now available. Due date: 03/03. Homework will be collected in the lecture. From the textbook: Section 3.1 (page 122): 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16. Section 3.2 (page 131): 1 (b), 1(c), 1(d), 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 10, 11 (b), 11(d), 11(e). 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. Section 3.4 (page 149): 2(b), 2(c), 2(e), 5, 7, 11, 12, 13, 16. If you want extra practice try 6, 8, 10, 14. Lecture 02/16 Section 2.2: Determinant of the product is the product of determinants. Sections 2.3: Determinant and the inverse matrix. Cross product. Sections 3.1: Vector spaces: definition and examples. Lecture 02/11 Sections 2.1: 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, computing the determinant through row operations. Condition on the determinant for non-singularity. Section 2.3: Cramer's rule. Lecture 02/09 Section 1.3: Transpose of a matrix, symmetric matrices. Sections 2.1: Determinants: 2x2 case, 3x3 case and general deinition. 2016/2/7, 11:35 Homework 4 now available. Due date: 02/18. Homework will be collected in the lecture. From the textbook: Section 2.1 (page 94): 1, 3, 4, 6, 9, 11. Section 2.2 (page 101): 2, 3(e), 3(f), 4, 5, 6, 7(c), 7(d), 10. If you want extra practice try 12. Section 2.3 (page 109): 1(c), 2(b), 2(d), 5, 9. 2016/2/4, 20:05 Lectures will be normal next week (T 02/09 and R 02/11). 2016/2/4, 13:55 Office Hours are cancelled next week (T 02/09 and W 02/10). Extra Office Hours this week: Friday 02/05 9-10 am Lecture 02/04 Sections 1.5: Matrix Inversion, Inverse of diagonal matrices, Inverse of 2x2 matrices, Compute the inverse using elementary row operations, Equivalent conditions for nonsingularity, Elementary matrices (and their inverses). Lecture 02/02 Sections 1.4: Matrix algebra: matrix multiplication, algebraic rules, Diagonal matrices, Identity matrix, Matrix Inversion. Lecture 01/28 Sections 1.3: Vectors, Matrix arithmetic: addition, scalar multiplication, Matrix multiplication and linear systems. 2016/2/2, 8:35 Homework 3 now available. Due date: 02/11. Homework will be collected in the lecture. From the textbook: Section 1.4 (page 56): 1, 3, 4, 5, 6, 7, 9, 11(a), 11(c), 11(d), 12, 13(c), 16, 17, 20, 24(b), 27, 30. Section 1.5 (page 66): 1, 5, 6, 9, 10(b), 10(c), 10(f), 10(g), 12(a), 12(d), 18. 2016/1/27, 12:40 Homework 2 now available. Due date: 02/04. Homework will be collected in the lecture. From the textbook: Section 1.2 (Applications - page 24): 15, 19, 21, 22(a), 22(c). Section 1.3 (page 42): 1(c), 1(e), 1(f), 1(g), 2(a), 2(b), 2(e), 2(f), 8(b), 8(c), 9, 10(a), 10(b), 13(a). Lecture 01/26 Section 1.2: Reduced Row Echelon Form, Consistency Check, Overdetermined/Underdetermined systems, Applications of systems of linear equations. Lecture 01/21 Sections 1.1, 1.2: Matrix, Coefficient and Augmented of a System, Elementary Row Operations, Row Echelon Form. 2016/1/20, 16:40 Homework 1 now available. Due date: 01/28. Homework will be collected in the lecture. From the textbook: Section 1.1 (page 10): 3(a), 3(d), 4, 5(b), 6(d), 6(h), 7, 8 (Use reduced row echelon form from Sec 1.2 instead of back substitution. Or try both ways.) and 9. Section 1.2 (exercises about applications will be required later)(page 24): 3(b), 3(d), 5(e), 5(f), 5(i), 6(b), 8, 10. Lecture 01/19 Section 1.1: Linear equation, system of linear equations, solutions of systems, 2x2 systems, equivalent systems, elementary operations. |