Linear Algebra with Differential Equations
Instructor: Waqas Ali Azhar (waqas.azhar@lums.edu.pk)
Class Schedule: Mon-Thu 2:00-3:40 PM SBASSE 10-201.
Office Hours: 1:00-2:00 PM SSE Mathematics Department 9-B-30.
TA Office Hours: TBA
Grading Breakdown:
Webwork: 10%
Quizzes: 25% (Every Thursday in Week 1,2,4,5)
Midterm: 25% (Thursday of Week 3) (In Class)
Final Examination: 40% (As per Zambeel)
Tips and Instructions
Choose a textbook. There are many good textbooks on linear algebra. Some popular choices include:
Linear Algebra with Applications by Gilbert Strang
Linear Algebra Done Right by Sheldon Axler
Elementary Linear Algebra by Howard Anton
Check your syllabus. A syllabus will provide you with a roadmap for the course. It will list the topics that will be covered, the assignments that will be due, and the grading rubric.
Set up a study schedule. It is important to set aside time each week to study linear algebra. Make a schedule that works for you and stick to it.
Join a study group. Studying with others can be a great way to learn linear algebra. Find a few classmates who are also taking the course and form a study group.
Attend office hours. If you are struggling with a concept, don't be afraid to ask for help. Your professor or TA will be happy to help you understand the material.
Practice, practice, practice. The best way to learn linear algebra is to practice. Do the assigned problems, and try to find additional problems to practice.
Don't give up. Linear algebra can be challenging, but it is also a rewarding subject. Don't give up if you find it difficult. Keep practicing and you will eventually master the material.
Here are some additional tips for taking a summer linear algebra course:
Start early. Don't wait until the last minute to start studying. Give yourself plenty of time to learn the material.
Take breaks. Don't try to study for hours on end. Take breaks every 20-30 minutes to avoid getting burned out.
Reward yourself. When you reach a milestone, reward yourself with something you enjoy. This will help you stay motivated.
Have fun! Linear algebra can be a lot of fun. Enjoy the challenge and the opportunity to learn a new subject.
Week 1: Linear systems, How do they appear in real settings (Fish problem, Equations balancing, traffic flow etc), Matrices and their algebra, Transpose, Trace. Solving linear systems, writing linear systems as matrix equations, geometry of solutions, echelon and reduced echelon forms.
Week 2: Elimination methods, Elementary matrices and inverses, LU Decomposition.
Quiz 1 Key
Week 3: Determinants, Properties, Cramer's rule, Vector spaces, Subspaces, Span.
Week 4: Linear Independence, Basis, Fundamental subspaces, Linear Transformations.
Week 5: Least squares, Eigenvalues/ Eigenvectors, Diagonalization, Introduction to ODEs.
Week 6: First order ODEs, Linear systems of Differential Equations and their solutions using Eigenvalues.
Math 120 Summer 24 Honoray List
