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Lorin Mandaloniz
MA-UY 1124 Calculus II for Engineers4 Credits This course covers techniques of integration, introduction to ordinary differential equations, improper integrals, numerical methods of integration, applications of integration, sequences, series, power series, approximations of functions via Taylor polynomials, Taylor series, functions of two variables, graphs of functions of two variables, contour diagrams, linear functions, functions of three variables. MA-UY 1424 is for students who wish to take MA-UY 1124 but need more review of precalculus. MA-UY 1424 covers the same material as MA-UY 1124 but with more contact hours per week, incorporating a full discussion of the required precalculus topics. Offered every term.
Prerequisite(s): MA-UY 1022 (with a grade of B or better) or MA-UY 1024 or MA-UY 1324 (with a grade of B or better). Corequisite(s): EX-UY 1 Examination Hour
Weekly Lecture Hours: 4 Weekly Lab Hours: 0 Weekly Recitation Hours: 0
MA-UY 1324 Integrated Calculus I for Engineers4 Credits This course covers: Library of Functions, functions of one variable. Limits, derivatives of functions defined by graphs, tables and formulas, differentiation rules for power, polynomial, exponential and logarithmic functions, derivatives of trigonometric functions, the product and quotient rules, the chain rule, applications of the chain rule, maxima and minima, optimization. The definite integral, the Fundamental Theorem of Calculus and interpretations, theorems about definite integrals, anti-derivatives. MA-UY 1324 is for students who wish to take MA-UY 1024 but need more review of precalculus. MA-UY 1324 covers the same material as MA-UY 1024 but with more contact hours per week, incorporating a full discussion of the required precalculus topics. Offered every term.
Prerequisite(s): Disgnostic exam or MA-UY 912 or MA-UY 914 . Corequisite(s): EX-UY 1 Examination Hour
Weekly Lecture Hours: 6 Weekly Lab Hours: 0 Weekly Recitation Hours: 0
Essentially a second course in calculus. Topics include techniques of integration, finding areas and volumes by integration, exponential growth, partial fractions, infinite sequences and series, tests of convergence, and power series.
Due to an overlap in content, students will not receive credit for both MATH 1120 and MATH 1910.PrerequisitesThree years of high school mathematics, including trigonometry and logarithms, and at least one course in differential and integral calculus, or equivalent AP credit. For guidance in selecting an appropriate course, please consult First Steps in Math.
This course covers both the theoretical foundations and practical applications of Vector Calculus. During the first week, students will learn about scalar and vector fields. In the second week, they will differentiate fields. The third week focuses on multidimensional integration and curvilinear coordinate systems. Line and surface integrals are covered in the fourth week, while the fifth week explores the fundamental theorems of vector calculus, including the gradient theorem, the divergence theorem, and Stokes' theorem. These theorems are essential for subjects in engineering such as Electromagnetism and Fluid Mechanics.
Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:
The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.
When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.
Topics in analytical geometry and calculus including limits, rates of change of functions, derivatives and integrals of algebraic and transcendental functions, applications of differentiations and integration. Note: GEEN 1350, a 1-credit lab, is available for students who would like more practice working calculus problems in a group learning environment. Requires prerequisite course of APPM 1235 or MATH 1021 or MATH 1150 or an ALEKS math score or 76% or greater. Students with credit in APPM 1350 may not receive credit for MATH 1080, 1081, 1090, 1100, 1300, 1310, or ECON 1088. Approved for arts and sciences core curriculum: quantitative reasoning and mathematical skills.
This unit's material is a collection of applications of integrals. The most important section, by far, is 6.7. In that section, we apply integrals to physical problems and start to get a sense of how useful this operation is in interpreting real-world processes.
In the rest of this unit's material we begin the study of methods of integration. There is a lot of material in this part of the course and it is important to be able to figure out when to use different methods, so make sure that you are careful in your studies of Chapter 7.
This unit, we look at two major methods of integration. Like all of the methods other than IBP, these are actually just subclasses of substitutions, but they are far from obvious and deserve separate treatment. There are a lot of things happening here and plenty of example videos in which to see these details in action. Go through the material carefully and remember that you want to be able to understand when to use each method.
This unit's material includes three very separate topics. We begin with numerical integration - another of the most important numerical methods we glance at in first year (together with Newton's method, linear approximation, and - soon - Taylor polynomials). The next section covers an interesting detail, looking at integrals that misbehave, either by having an unbounded integrand or an unbounded interval. Either way, the solution is to use limits. Finally, we begin to study differential equations, which are the basis for a tremendous amount of engineering.
We begin in earnest our study of differential equations. These tremendously useful tools for science and engineering end up being rather pesky in terms of the ways we go about solving them. In this unit, we will be introduced to two types of DEs, as well as a numerical method for approximating solutions.
In this unit, we finish our study of differential equations. This includes a small section on second-order equations. The Briggs textbook includes an electronic-only chapter on these and we include it here. We will only be looking at the first two sections of that chapter (and, even then, only the aspects covered in the lecture videos).
Through the three sections in this unit and the two sections in the next, we look at a few definitions and then study when series converge and diverge. We discover a number of tests that will help us figure out this information, including some very unusual-looking ones. The goal of this chapter is to allow us to use the information here when we try to express functions using certain infinite polynomials (we will call them power series). Knowing when a series converges or diverges will let us find out when our power series exist.
In the sections covered in this unit, we do two things. First, we examine more convergence tests on positive (or non-negative) series. The tests range from ugly to beautiful, but are all useful. In the second section, we open up to the idea of allowing negative terms in our series and find that this leads to some very odd complications.
We begin our study of Taylor Series by looking at each half of the phrase individually - first we study (finite) Taylor polynomials. Then, before we extend them forever, we look at how series with a variable behave.
In this chapter, we start examining the effect of having an independent variable determine two (and, in the next chapter, three) dependent coordinates. The most common applications are those in which we use the parameter of time to describe physical motion through the plane and through space.
The beginning of the study of vector-valued functions mirrors precisely the study of parametric equations. Most of the material in this week is nearly identical to what we had in the previous chapter.
The material here takes us to the end of the course. I have included an extra section on multivariable calculus - simply an idea of what a multivariable function is and how to take partial derivatives.
The Math Placement Exam 4 (MPE4) will determine which math course you are placed in for your first semester at Texas A&M University. Proper placement in your first math course is critical to your success in the College of Engineering. The MPE4 is offered in an online, proctored setting via Zoom. All students admitted to the College of Engineering (COE) must complete their MPE4 prior to attending their New Student Conference. Testing for new COE students admitted for Fall 2024 will begin on May 13 and continue through early June. Exam date availability is on a first-come, first-serve basis, so please do not delay. The earlier you complete your exam, the more options you will have to become calculus ready for the fall semester.
The MPE4 is an online 33-question, non-calculator exam that takes 90 minutes to complete. It will test your knowledge of algebra, trigonometry, logarithms, exponentials, etc. While it does not test your calculus knowledge, you should take it seriously and prepare for the exam well ahead of your scheduled testing date (i.e., review material, self-study and take practice exams).
For General Engineering students: Scoring 22 (67%) or higher on the MPE4 and demonstrating readiness to enroll in Calculus I (MATH 151) during your first semester in the College of Engineering is the first step toward earning your engineering degree within four years. You should do everything you can to be calculus-ready by the time you begin classes.
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