Our averages were drastically low, not to mention it was really difficult to understand her lectures as they were never clear. Exams reflected nothing that was taught in class.

I would not recommend this class with Biswal. Positive aspects: Biswal was helpful during office hours, gave engaging lectures, and gave exams that were easy/medium. However, there were also quite a few negative aspects.
Lectures were chaotic, as Biswal would consistently make errors during them. There was almost always a notation or algebra-related error on the board, and Biswal would make changes to what she wrote very often, making it difficult to take notes. Additionally, she made errors while explaining the analysis behind the diff eq concepts, which I found to be concerning (for example, she butchered the definition of injective/one-to-one, something that any math major would have seen in 33A, 115A, and/or 131A). When someone in class would speak up about these errors, she would get angry and make condescending/rude comments, such as, "I have to remind myself to never use advanced math notation around my students."
Homework assignments were long and unnecessarily difficult. The textbook was extremely unhelpful, and I found myself having to teach myself how to apply what was covered in the lectures to the homework problems. Biswal also gave few to no resources to study with for her exams, and when she gave practice problems, they were very difficult (more so than the actual exam) with no solutions, and the textbook has no practice problems that are of appropriate difficulty for the exam, so it was very difficult to study for this class as well.
Between the chaotic lectures and rude commentary on Biswal's behalf, the lack of study resources, and the very long and hard homework assignments, I would recommend staying away from this professor if you can.

This was a horrible class. I entered the class with some knowledge of the topics, including a working understanding of Fourier analysis (including the applications to differential equations) and Laplace transforms. When the professor was talking about these concepts, I could tell that she was making so many extremely misleading statements, so I was not surprised when I wasn't able to understand the material that I did not know beforehand. She stresses the importance of rigor that one is expected to learn in an analysis class like 131A, and then in the very next sentence she will violate every rule possible. This ends up being much more than technicalities, to the point where it becomes difficult to decipher the actual argument she is trying to make.

Prof. Biswal is not inclusive: she tends to almost mockingly single out people in lecture under the pretext of "encouraging involvement." She makes gender-binary (i.e. male-female) examples when trying to explain concepts. She openly said so many condescending stuff about how inept students in her math 134 class (which she was teaching during the same quarter as 135) were.

She prefaced her discussion of partial differential equations with comments about how she does not enjoy the topic, and how she's upset her present advisor recommended she undertake research about PDEs. It made the vibes horrible: how can students enjoy a course that the professor expresses a disinterest in?

The course is graded on a very harsh curve.

The textbook (by Simmons) is poorly structured and lacks rigor; the professor spends a lot of time talking about her dislike for the textbook.

131A (analysis) is not listed as a co- or pre-requisite, but prof. Biswal assumes you are familiar with several concepts from that course, particularly regarding continuity and convergence. However, I'd taken 131A the previous quarter, and my professor skipped the discussion of some aspects of continuity and convergence that were important for 135. Prof. Biswal spend so much time talking about not wanting to review the relevant 131A topics that it would have been more efficient for her to just take a stab at them. I wasn't able to make her office hours time, so I watched several video lectures and read the section from Ross's analysis book; Biswal was willing to give us some homework problems about the analysis material, but they were very very shallow (literally just testing definitions) and they did not help build the level of understanding required for the class.

She does not release solutions to the homework problems, which, in my opinion, sort of destroys the point. Many of the problems are not even graded, and those that are receive very little feedback about what the right answer is.

Although Biswal gets some credit for emphatically saying she wants to help, the fact remains that she simply does not make the class engaging and her lectures are extremely poor.

Math 135 is on the more conceptual side and so is Prof Biswal's teaching style. The class emphasizes heavily on linear algebra basics from Math 115A. Math 131A is definitely recommended before this class. While the lecture may not be clear at times, Prof Biswal is extremely helpful after the class - she would answer every question on campuswire and send follow-ups for your questions. The homework is more computation-heavy as compared to the exams, which place heavy emphasis on making conceptual connections. Overall, I find the class to be very enjoyable.

The Subject Matter:
Math 135 is very different from the Lower Division Differential Equations course, but if you enjoy diff. eq.s, I'm pretty sure you'll enjoy this class. The class aims to teach you more of the theory behind diff. eq.s rather than emphasizing memorization of techniques. Over the course of the quarter, you will use concepts from linear algebra (basis, self-adjointness, and orthogonality mainly), and I believe some experience with real analysis (convergence of series, sequences, etc.) would provide a more complete understanding of the topics. As a warning, some of the topics of the class are somewhat difficult to fully grasp due to their nuance.

Prof. Biswal:
Professor Biswal makes sure lectures are engaging for students by asking the class questions. To me, this is an extremely effective way of solidifying student understanding--you'll be able to recognize the gaps in your understanding by trying to explain your thoughts precisely and succinctly to Prof. ! Prof. is also very kind, helpful, and patient which goes a long way to encourage students to ask questions. Overall, she is a great professor!

Homework:
The homework load is very manageable and consists mainly of problems from the textbook.

Exams:
Exams are somewhat difficult, and sometimes the questions don't reflect problems discussed in lecture or asked of you on homework assignments. However, you can cleverly use the topics in the class to find the answers to these sometimes perplexing exam problems.

Math 135 is kind of a confusing class. The professor doesn't really deeply cover the material that's on exams and homework, and so you're left to teach yourself the nit and grit of the course. I think if you're really math minded, and have experience from courses like Math 131 and Math 115 you should be fine in this class because some of the topics do relate to matters from those classes. If you aren't super math-y and don't have a lot of experience in math upper divs, some topics will be harder to master. If you're really willing to put in the time to learn the material (by finding supplemental stuff online) or go to OH, this class is pretty doable. Biswal is really nice and is always ready to answer questions.

Literally do NOT take her. 0/10.