Just about all of calculus is based on differential and integral calculus, including Calculus 1! However, Calculus 1 is more likely to cover differential calculus, with integral calculus soon after. So there really isn't a right answer for this question.
John Philips Higman has written: 'A syllabus of the differential and integral calculus' -- subject(s): Calculus, Integral, Differential calculus, Integral Calculus
Alfred Lodge has written: 'Integral calculus for beginners' -- subject(s): Calculus, Integral, Integral Calculus 'Differential calculus for beginners' -- subject(s): Differential calculus
Differential calculus is concerned with finding the slope of a curve at different points. Integral calculus is concerned with finding the area under a curve.
Differential Calculus, Integral Calculus, Vector Calculus and Differential Equations are required for any engineering field.
George A. Osborne has written: 'An elementrary treatise on the differential and integral calculus' -- subject(s): Calculus 'The integral calculus applied to plane curves' -- subject(s): Integral Calculus
Calculus, both differential and integral.
One directly undoes the process of the other.
T. G. Hall has written: 'A treatise on the differential and integral calculus' -- subject(s): Calculus
People often divide Calculus into integral and differential calculus. In introductory calculus classes, differential calculus usually involves learning about derivatives, rates of change, max and min and optimization problems and many other topics that use differentiation. Integral calculus deals with antiderivatives or integrals. There are definite and indefinite integrals. These are used in calculating areas under or between curves. They are also used for volumes and length of curves and many other things that involve sums or integrals. There are thousands and thousand of applications of both integral and differential calculus.
Edward H. Courtenay has written: 'A treatise on the differential and integral calculus, and on the calculus of variations' -- subject(s): Accessible book, Calculus
the example and solution of integral calculus
That would be Leibniz.
Differential and Integral Calculus, Universal Gravitation, Telescope, White Light Composition
G. Greenhill has written: 'Differential and integral calculus' -- subject(s): Calculus 'The third elliptic integral and the ellipsotomic problem' 'Gyroscopic theory'
L S. Hulbert has written: 'Differential and integral calculus'
Catherinus Putnam Buckingham has written: 'Elements of the differential and integral calculus' -- subject(s): Accessible book, Calculus
Gottfried Leibniz is called the father of integral calculus.
A first year student would use mechanics, geometry, trigonometry, coordinate geometry, algebra, differential calculus, integral calculus.
Martin Lindow has written: 'Differentialrechnung' -- subject(s): Differential calculus 'Integralrechnung' -- subject(s): Integral Calculus
The foundation, in both cases, is the concept of limits. Calculus may be said to be the "study of limits". You can apply a lot of calculus in practice without worrying too much about limits; but then we would be talking about practical applications, not about the foundation.
Integral calculus was invented in the 17th century with the independent discovery of the fundamental theorem of calculus by Newton and Leibniz.
Analysis is a broader term for Calculus and the theorems behind it. It is studied both with real and complex numbers as real and complex analysis. Usually calculus just deals with the basic problems of differential calculus and integral calculus.
William F. Osgood has written: 'A first course in the differential and integral calculus'
You must have a strong basis in Algebra, Algebra II, Geometry and Trigonometry. Usually high schools offer a pre-Calculus course which is somewhat of a conglomeration of the aforementioned courses. Then you would move into differential calculus, integral calculus, vector (multi-variable) calculus, and finally differential equations, which is considered to be at the top of the hierarchy of the calculus courses. So take Algebra, Algebra II, Geometry and Trigonometry to get your strong foundation before begining the calculus sequence.