Calculus II

Description of Course Goals and Curriculum

MAT 104 demands familiarity of mathematical concepts from Calculus I or MAT103: integration, differentiation, limits, integrals, trigonometric properties, the Fundamental Theorem of Calculus, and graphing techniques. The goal of the course is to improve students’ problem-solving abilities through examples and problems covered in lectures, problem sets, and exams and quizzes. The course expounds on the curriculum of MAT103, but additionally focuses on infinite series, differential equations, and Taylor Series. The course increases in difficulty, as topics become more complex. Similarly, the questions posed within each section will increase in difficulty, as the course aims to push students to apply more basic concepts towards more difficult problems, some of which may not be covered in class. The goal of the course’s progression in complexity is to develop critical thinking skills. Students are expected to quickly recall trigonometric functions, equations, and techniques, in exam settings. It is beneficial to do the homework in advance, prepare questions, and become quite familiar with the material. The course does not allow equation sheets or calculators, so it is important that students are quite fluent in the course material. The course requires retention of material for the entirety of the course. It is critical to learn for retention rather than to simply complete assignments. Students are expected to prove their grasp of the material by clearly showing their work. Some answers may be written out, while others may be numerical. MAT104 requires a great attention to detail; correct notation and descriptions are required alongside correct answers.

Learning From Classroom Instruction

Lecture- The pace of lectures depends on the professor; however, in general, lectures will focus on examples that highlight specific patterns that should eventually become intuitive. Overall, the course goes at a fast pace, so it is advised to stay up to date on the curriculum. Fundamentals are taken as a given. Material that comes down to rote memorization is best to be attained in the beginning weeks of the course. This relates to concepts like trig identities, algebraic manipulation, and concepts from Calculus I or MAT103. It is helpful to review the concepts that will be covered in lecture, before going to lecture. Often, students feel inundated with information that has little tangible value, in the sense that the terminology and processes are foreign. Taking 30 minutes to familiarize oneself with the basic computations and logic of the lectures, before attending will make lectures more valuable. It is important to write down all example problems and their steps in class, marking any steps that you don’t quite understand. This makes studying more focused and personalized. Students are expected to read the textbook, before coming to lecture. Because lecturers will work through example problems, it is beneficial to focus mainly on example problems and solutions in the textbook, working through the problems yourself. The readings are particularly helpful for homework problems because the chapters that correspond with certain questions often contain clarifying descriptions. Sometimes, students will be expected to complete homework questions that are not covered in lecture, but are solely covered in the textbook. While the lecturer will go over these homework questions, after the assignments are graded, it is important to read the textbook to solve these problems. Each instructor has weekly office hours that allow for one on one questions. Students can attend multiple office hours from any of the instructors for the course, so it is alright if you cannot make your own instructor’s hours. Akin to a precept, it is beneficial to come to office hours prepared. Have questions prepared for specific concepts or steps that you would like clarified. This is a great space to ask exam questions, homework questions, and/or general questions. Another great resource is weekly review sessions. If you are stuck on a homework problem, or would like to see more examples of questions from ranging topics, this is the perfect setting to do so. Before each exam, a review session will be held, and many important insights into exam questions will be covered.

Learning For and From Assignments

Problem sets are used to expand on students’ application of ideas that are covered in lecture. The homework problems will typically increase in difficulty as throughout the problem set. Similarly, application of concepts will be more complex and extensive on exams. Application and pattern detection is a large portion of the course. Doing as much of each problem as possible and doing the problem sets over a period of several days is preferable, as you have more time to think and prepare questions in lecture or office hours. Saving lengthy assignments for the last minute will not allow sufficient time for concepts to truly set in. The course demands adequate attention to detail and long term memorization. For example, rather than memorizing trigonometric rules, it is possibly more beneficial to understand their derivations, to understand different tricks and strategies that will allow one to manipulate the prompts. Students often ask how one is supposed to derive such creative solutions to problems, and the answer is practice. Lecture examples may closely resemble portions of problems; however, the problem set questions will be of a greater difficulty. On exams and quizzes, basic concepts will be combined and interspersed in much more difficult problems. This course relies heavily on creativity and a strong foundation in manipulating problems into more manageable pieces. When working on problem sets, it is beneficial to note the purpose or goal of more challenging problems: the more difficult problems aim to extract the most pertinent concepts of more basic problems. Being confident in processes and familiar with unique techniques for solving problems is beneficial. Practice and attention to the process of problems will make exams more manageable. Furthermore, it is helpful to do practice exams and practice problems, before exams; reviewing as many homework problems as one can, especially problems that caused trouble, keeps studying more focused and purposeful.

External Resources

Sources like Khan Academy can be helpful for getting a quick summation of certain topics, or a different perspective on problems. The McGraw Learning Program is a great resource on campus that offers peer tutoring.

What Students Should Know About This Course For Purposes Of Course Selection

Though this course is a requirement for certain majors, it is also a great class to expound on one’s critical thinking and application skills through Calculus II concepts. Many courses at Princeton will push students to think more critically and beyond tasks that require basic application skills and memorization, although these skills are useful. Do not be intimidated by the course, if you qualify to take it based on AP and high school preparation. Math courses build on one another, so there is no need to retake MAT103, if you have already successfully mastered concepts of Calculus I.