# Calculus Sequences

# Calculus Sequences

- MATH 115 - 116
- MATH 125 - 126 - 127
- MATH 145 - 146 - 147
- 200-level Math Courses
- Old Calculus Sequence

## MATH 115 - 116 Calculus I, II. 3 credits each

### Prerequisites

For MATH 115: MATH 101, or MATH 104, or two years of high school algebra and a score of 26 or higher on the ACT mathematics, or a qualifying score on the mathematics placement test.

For MATH 116: MATH 115, plus a course in trigonometry, or MATH 121 or MATH 125. MATH 103 may be taken concurrently.

### Purpose of sequence

This calculus sequence is intended for students who do not plan to take more mathematics courses. Many students take MATH 115 by itself to satisfy the Core quantitative literacy requirement or the CLAS BA second-level quantitative requirement, or to satisfy a requirement for a biology major. Pre-business students generally take MATH 115. Economics BA students can satisfy their calculus requirement with MATH 115 - 116, but Economics BS students need MATH 125 - 126 - 127.

### Course content

MATH 115 covers limits, derivatives, exponential and logarithmic functions, antiderivatives and applications. Trigonometric functions are not used in MATH 115.

MATH 116 covers integration, the calculus of trigonometric functions, partial derivatives, multiple integrals and infinite series.

### Trigonometry

Trigonometry is not a prerequisite for MATH 115 and trigonometric functions are not used in MATH 115.
*Trigonometry is a prerequisite for MATH 116.*
Students without a good high school trigonometry course should take MATH 103 Trigonometry (2 credits) in the fall semester.

### Substitution for MATH 125

A student can enroll in MATH 126 Calculus II, but not MATH 127 Calculus III, after taking MATH 116. MATH 115 - 116 cover most of the topics of MATH 125 and some topics of MATH 126 and MATH 127, but not in the depth of the MATH 125-127 sequence. For this reason, students considering taking MATH 126 in the future are strongly encouraged to start calculus in MATH 125.

### Format

MATH 115 is taught in small sections (under 40 students). All students in MATH 115 take the same midterm and final exams. Consult the timetable for the time of these exams.

MATH 116 is taught in either a large lecture (up to 175 students) or in a small section. There are no common exams.

Both courses are offered online as well.

## MATH 125 - 126 - 127 Calculus I, II, III. 4 credits each

### Prerequisites

For MATH 125: MATH 103 or 104 with a grade of C- or higher, or three years of college preparatory mathematics including trigonometry and a score of 28 or higher on ACT mathematics, or a qualifying score on the mathematics placement test.

For MATH 126: MATH 125, MATH 145, or MATH 116 with a grade of C- or better. (Students who have completed MATH 116 earn only 2 additional credits for MATH 126.)

For MATH 127: MATH 126 or MATH 146 with a grade of C- or better.

### Purpose of sequence

This calculus sequence is intended for math, science, and engineering majors. Anyone considering going beyond Calculus II should take this sequence.

## Course content

MATH 125 covers limits, derivatives, applications of differentiation, the integral and basic applications of the integral, and uses exponential, logarithmic and trigonometric functions.

MATH 126 covers techniques of integration, applications of integration, infinite sequences and series, polar coordinates, vector geometry, and an introduction to differential equations.

MATH 127 covers multivariable and vector-valued functions, partial derivatives, multiple integrals and vector calculus, including Green's and Stokes's Theorems.

### Format

MATH 125 through 127 are taught as a Lecture-Lab course. Students attend a large lecture (175 - 250 students) three times per week and a small lab section (30 - 35 students) twice per week. All students in each course take the same midterms and final exams. Consult the timetable for the time of these exams.

## MATH 145 - 146 - 147 Calculus I, II, III Honors. 4 credits each

### Prerequisites

In addition to the prerequisites for MATH 125 - 126 - 127, students must qualify for the honors courses as follows.

Students new to KU: Students with a score of 34 or more on ACT mathematics, or a score of 32 or more on ACT mathematics and membership in the University Honors Program, are invited to enroll in MATH 145, or in MATH 146 or MATH 147 if they have AP or transfer credit for the prerequisite courses.

Continuing KU students: Students who have taken mathematics courses at KU are invited to subsequent honors courses upon recommendation of their KU instructors.

### Purpose of sequence

This calculus sequence is intended for strong students who wish to study mathematics in more depth and who are seeking mathematical challenge.

### Course content

MATH 145 - 146 - 147 cover the MATH 125 - 126 - 127 syllabi, and use the same textbook. In addition, the instructors may choose to study calculus topics in greater depth or to incorporate enrichment materials from various areas of mathematics. Qualifying students are encouraged to choose the Honors courses if they wish a greater mathematical challenge.

### Format

MATH 145 through 147 are taught in small sections (under 40 students). The final exams are at the same time as the MATH 125 through 127 exams. Consult with the instructor for the scheduling of the midterm exams.

## 200-level Math Courses

The following courses have a MATH 126 prerequisite: upper division courses generally have one or both of these, along with MATH 127, as prerequisites.

- MATH 220 Applied Differential Equations (3 credits); MATH 221, Honors
- MATH 290 Elementary Linear Algebra (2 credits); MATH 291, Honors

It is strongly recommended that students take MATH 290 before or at the same time as MATH 220.

MATH 320 Elementary Differential Equations is recommended in place of MATH 220 for students majoring in mathematics, astronomy, atmospheric science, and physics. It is to be taken after MATH 127 and MATH 290.

## Old Calculus Sequence

MATH 121 - 122 Calculus I, II (5 credits each) and MATH 223 Vector Calculus (3 credits) (and Honors MATH 141, 142, 243)

This sequence was offered for the last time in the 2015-16 academic year. MATH 121 covered all material in MATH 125 plus all material on integration techniques and applications of integration, now in MATH 126. MATH 122 covered the remaining material in MATH 126 and the multivariable calculus now in MATH 127. MATH 223 covered multivariable calculus and vector calculus, going beyond MATH 127.