Calculus of variations

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This document is an introduction to calculus of variations presented by Abdelmottalib Albayrouni. It contains mathematical expressions and functions related to calculus of variations including integrals involving functions between limits and functional notations for curves. Students can find courses on this topic starting in September 2019 on the website udemy.com from the Effective Learning program.

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Calculus of variations : AN INTRODUCTON
EFFECTIVE LEARNING: ﬁnd our courses on udemy.com
starting september 2019
Presented by:
ABDELMOTTALIB ALBAYROUNI
moghaﬀal@gmail.com
EFFECTIVE LEARNING: ﬁnd our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON

Calculus of variations
EFFECTIVE LEARNING: ﬁnd our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON

Calculus of variations
B(c, d) A(a, b)
EFFECTIVE LEARNING: ﬁnd our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON

Calculus of variations
A(a1, a2, a3) φ(x, y, z) = 0
B(b1, b2, b3)
EFFECTIVE LEARNING: ﬁnd our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON

Calculus of variations
B(b, 0) A(a, 0) y = f (x)
f
EFFECTIVE LEARNING: ﬁnd our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON

Calculus of variations
[a, b] y = f (x)
[a, b] y = g(x)
EFFECTIVE LEARNING: ﬁnd our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON

Calculus of variations
A(0, 0); B(a, 0); C(a, a); D(0, a)
C((a, a), R = a)
EFFECTIVE LEARNING: ﬁnd our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON

Calculus of variations
C(a, b)
C(b, a)
EFFECTIVE LEARNING: ﬁnd our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON

Calculus of variations
v(y(x)) =
x1
x0
y(1 + y 2)
EFFECTIVE LEARNING: ﬁnd our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON

Calculus of variations
v(y(x)) =
x1
x0
y
EFFECTIVE LEARNING: ﬁnd our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON

Calculus of variations
v(y(x)) =
x1
x0
y + y2
EFFECTIVE LEARNING: ﬁnd our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON

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Calculus of variations

1. Calculus of variations : AN INTRODUCTON EFFECTIVE LEARNING: find our courses on udemy.com starting september 2019 Presented by: ABDELMOTTALIB ALBAYROUNI moghaff[email protected] EFFECTIVE LEARNING: find our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON

2. Calculus of variations EFFECTIVE LEARNING: ﬁnd our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON

3. Calculus of variations B(c, d) A(a, b) EFFECTIVE LEARNING: ﬁnd our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON

4. Calculus of variations A(a1, a2, a3) φ(x, y, z) = 0 B(b1, b2, b3) EFFECTIVE LEARNING: ﬁnd our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON

5. Calculus of variations B(b, 0) A(a, 0) y = f (x) f EFFECTIVE LEARNING: ﬁnd our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON

6. Calculus of variations EFFECTIVE LEARNING: ﬁnd our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON

7. Calculus of variations EFFECTIVE LEARNING: ﬁnd our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON

8. Calculus of variations EFFECTIVE LEARNING: ﬁnd our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON

9. Calculus of variations EFFECTIVE LEARNING: ﬁnd our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON

10. Calculus of variations EFFECTIVE LEARNING: ﬁnd our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON

11. Calculus of variations [a, b] y = f (x) [a, b] y = g(x) EFFECTIVE LEARNING: ﬁnd our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON

12. Calculus of variations A(0, 0); B(a, 0); C(a, a); D(0, a) C((a, a), R = a) EFFECTIVE LEARNING: ﬁnd our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON

13. Calculus of variations C(a, b) C(b, a) EFFECTIVE LEARNING: ﬁnd our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON

14. Calculus of variations v(y(x)) = x1 x0 y(1 + y 2) EFFECTIVE LEARNING: ﬁnd our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON

15. Calculus of variations v(y(x)) = x1 x0 y EFFECTIVE LEARNING: ﬁnd our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON

16. Calculus of variations v(y(x)) = x1 x0 y + y2 EFFECTIVE LEARNING: ﬁnd our courses on udemy.com starting september 2019Calculus of variations : AN INTRODUCTON